A355603 Expansion of e.g.f. (1 + x)^(x^4/24).

1, 0, 0, 0, 0, 5, -15, 70, -420, 3024, -22050, 202950, -2113650, 24324300, -305645340, 4174483950, -61253992800, 961049212200, -16054949350440, 284505099278400, -5329752594075000, 105239780964864000, -2184466455408699000, 47550052231211237400

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

Cf. A007113, A355605.

Sequence in context: A149639 A149640 A353173 * A355507 A259205 A149641

Adjacent sequences: A355600 A355601 A355602 * A355604 A355605 A355606

Keyword

sign

Author

Seiichi Manyama, Jul 09 2022

Status

approved