OFFSET
0,6
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..451
FORMULA
a(0) = 1; a(n) = -(n-1)!/24 * Sum_{k=5..n} (-1)^k * k/(k-4) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/5)} Stirling1(n-4*k,k)/(24^k * (n-4*k)!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x)^(x^4/24)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^4/24*log(1+x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-(i-1)!/24*sum(j=5, i, (-1)^j*j/(j-4)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\5, stirling(n-4*k, k, 1)/(24^k*(n-4*k)!));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 09 2022
STATUS
approved