A352073 Expansion of e.g.f. 1/(1 - log(1 + 4*x))^(1/4).
1, 1, 1, 17, 1, 1889, -12415, 631665, -11224575, 461864385, -13754112255, 596055636945, -24148300842495, 1181210529292065, -59009709972278655, 3297137505670374705, -193318225258785780735, 12263541239089421903745, -820804950905249837195775
Offset: 0
Keywords
Programs
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Mathematica
m = 18; Range[0, m]! * CoefficientList[Series[(1 - Log[1 + 4*x])^(-1/4), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+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, 1));
Formula
a(n) = Sum_{k=0..n} 4^(n-k) * (Product_{j=0..k-1} (4*j+1)) * Stirling1(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-4)^k * (3/4 * k/n - 1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Nov 18 2023