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A223173
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Poly-Cauchy numbers c_3^(-n).
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2
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-1, -3, -1, 45, 359, 2037, 10079, 46365, 204119, 873477, 3666959, 15191085, 62342279, 254119317, 1030760639, 4165958205, 16792710839, 67557739557, 271392171119, 1089053371725, 4366669645799, 17498051254197, 70086331418399, 280627721655645
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OFFSET
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1,2
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COMMENTS
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Definition of poly-Cauchy numbers in A222627.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..3} Stirling1(3,k)*(k+1)^n.
Conjecture:
a(n) = 2^(1+n) - 3^(1+n) + 4^n;
g.f.: -x*(6*x-1) / ((2*x-1)*(3*x-1)*(4*x-1)). (End)
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MAPLE
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MATHEMATICA
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Table[Sum[StirlingS1[3, k] (k + 1)^n, {k, 0, 3}], {n, 25}]
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PROG
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(Magma) [&+[StirlingFirst(3, k)*(k+1)^n: k in [0..3]]: n in [1..25]]; // Bruno Berselli, Mar 28 2013
(PARI) a(n) = sum(k=0, 3, stirling(3, k, 1)*(k+1)^n); \\ Michel Marcus, Nov 14 2015
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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