OFFSET
0,4
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
MATHEMATICA
m = 18; Range[0, m]! * CoefficientList[Series[(1 - Log[1 + 4*x])^(-1/4), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
PROG
(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));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 05 2022
STATUS
approved