A353344 Expansion of e.g.f. exp(-log(1 - x)^3).

1, 0, 0, 6, 36, 210, 1710, 17304, 194712, 2402184, 32536080, 481094856, 7703580456, 132658888752, 2443228469136, 47904722262144, 995970495769920, 21879712141853760, 506301721998264000, 12306713585213260800, 313441368701926135680, 8345931596469584686080

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..442

Formula

E.g.f.: (1 - x)^(-(log(1 - x))^2).

a(0) = 1; a(n) = 6 * Sum_{k=1..n} binomial(n-1,k-1) * |Stirling1(k,3)| * a(n-k).

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * |Stirling1(n,3*k)|/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x)^3)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-log(1-x)^2)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=6*sum(j=1, i, binomial(i-1, j-1)*abs(stirling(j, 3, 1))*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\3, (3*k)!*abs(stirling(n, 3*k, 1))/k!);

Crossrefs

Column k=3 of A357882.

Cf. A000142, A353358, A353404.

Cf. A347002, A353118, A353664.

Sequence in context: A105492 A052748 A292297 * A353118 A357027 A357093

Adjacent sequences: A353341 A353342 A353343 * A353345 A353346 A353347

Keyword

nonn

Author

Seiichi Manyama, May 06 2022

Status

approved