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A051782
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Apply the "Stirling-Bernoulli transform" to Catalan numbers.
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2
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1, 0, 2, -12, 122, -1620, 26882, -536172, 12506762, -334261380, 10075002962, -338180323932, 12512502202202, -505992958647540, 22204726014875042, -1050993549782729292, 53373431773793542442, -2894886293042487680100, 167021024758368026331122
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OFFSET
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0,3
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COMMENTS
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The "Stirling-Bernoulli transform" maps a sequence b_0, b_1, b_2, ... to a sequence c_0, c_1, c_2, ..., where if B has o.g.f. B(x), c has e.g.f. exp(x)*B(1-exp(x)). More explicitly, c_n = Sum_{m=0..n} (-1)^m*m!*Stirling2(n+1,m+1)*b_m.
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LINKS
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FORMULA
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MAPLE
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a:= n-> add((-1)^k *k! *Stirling2(n+1, k+1)*binomial(2*k, k)/
(k+1), k=0..n):
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MATHEMATICA
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a[n_] := Sum[(-1)^k k! StirlingS2[n+1, k+1] CatalanNumber[k], {k, 0, n}];
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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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