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A003713
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Expansion of e.g.f. log(1/(1+log(1-x))).
(Formerly M1799 N0710)
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33
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0, 1, 2, 7, 35, 228, 1834, 17582, 195866, 2487832, 35499576, 562356672, 9794156448, 186025364016, 3826961710272, 84775065603888, 2011929826983504, 50929108873336320, 1369732445916318336, 39005083331889816960, 1172419218038422659456, 37095226237402478348544
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OFFSET
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0,3
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COMMENTS
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a(n+1) is the permanent of the n X n matrix M with M(i,i) = i+1, other entries 1. - Philippe Deléham, Nov 03 2005
Unsigned coefficients for the raising / creation operator R for the Appell sequence of polynomials A238385: R = x + 1 - 2 D + 7 D^2/2! - 35 D^3/3! + ... . - Tom Copeland, May 09 2016
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REFERENCES
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J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n+1) = n! * Sum_{k=0..n} A007840(k)/k!. E.g., a(4) = 228 = 24*(1/1 + 1/1 + 3/2 + 14/6 + 88/24) = 24 + 24 + 36 + 56 + 88. - Philippe Deléham, Dec 10 2003
a(0) = 0; a(n) = (n-1)! + Sum_{k=1..n-1} binomial(n-1,k) * (k-1)! * a(n-k). - Ilya Gutkovskiy, Jul 18 2020
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MAPLE
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series(ln(1/(1+ln(1-x))), x, 17);
with (combstruct): M[ 1798 ] := [ A, {A=Cycle(Cycle(Z))}, labeled ]:
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Log[1/(1+Log[1-x])], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Dec 15 2012 *)
Table[Sum[(-1)^(n-k) * (k-1)! * StirlingS1[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 19 2024 *)
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PROG
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(PARI) a(n)=if(n<0, 0, n!*polcoeff(-log(1+log(1-x+x*O(x^n))), n))
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CROSSREFS
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KEYWORD
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nonn,easy,nice,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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