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A352123
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Expansion of e.g.f. (2 - exp(-4*x))^(1/4).
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2
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1, 1, -7, 73, -1135, 24241, -659767, 21796153, -846456415, 37772943841, -1904103268327, 106992035096233, -6630198107231695, 449171668238551441, -33024202381308836887, 2618743082761141212313, -222782402553043700662975, 20238957866498067052271041
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-4)^(n-k) * (Product_{j=0..k-1} (-4*j+1)) * Stirling2(n,k).
a(n) ~ n! * (-1)^(n+1) * Gamma(1/4) * 2^(2*n - 9/4) / (Pi * n^(5/4) * log(2)^(n -1/4)). - Vaclav Kotesovec, Mar 06 2022
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MATHEMATICA
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m = 17; Range[0, m]! * CoefficientList[Series[(2 - Exp[-4*x])^(1/4), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((2-exp(-4*x))^(1/4)))
(PARI) a(n) = sum(k=0, n, (-4)^(n-k)*prod(j=0, k-1, -4*j+1)*stirling(n, k, 2));
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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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