A354318 Expansion of e.g.f. exp(-log(1 + x)^4 / 24).

1, 0, 0, 0, -1, 10, -85, 735, -6734, 66024, -693230, 7774250, -92754046, 1172033148, -15609023066, 217966080150, -3173198858894, 47842246890224, -740798341880328, 11644416638285544, -182433719522266066, 2752864573552860900, -36826753489645422050

Offset

0,6

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: 1/(1 + x)^(log(1 + x)^3 / 24).

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling1(k,4) * a(n-k).

a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling1(n,4*k)/((-24)^k * k!).

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[-Log[1+x]^4/24], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 27 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1+x)^4/24)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x)^(log(1+x)^3/24)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i-1, j-1)*stirling(j, 4, 1)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 1)/((-24)^k*k!));

Crossrefs

Cf. A346946, A347003, A354317.

Sequence in context: A233667 A038235 A354390 * A346946 A000454 A347003

Adjacent sequences: A354315 A354316 A354317 * A354319 A354320 A354321

Keyword

sign

Author

Seiichi Manyama, May 24 2022

Status

approved