A354134 Expansion of e.g.f. 1/(1 - log(1 + x)^3/6).

1, 0, 0, 1, -6, 35, -205, 1204, -6692, 29084, 17160, -3069924, 61356724, -959574408, 13499619224, -174983776176, 2029529618080, -18417948918640, 36189097244720, 4235753092128480, -157628320980720480, 4166967770825777280, -95152715945973322560

Offset

0,5

Links

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

Formula

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

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling1(n,3*k)/6^k.

Prog

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

Crossrefs

Cf. A006252, A354135.

Cf. A346894, A346922.

Sequence in context: A001109 A352972 A180033 * A260770 A262717 A144638

Adjacent sequences: A354131 A354132 A354133 * A354135 A354136 A354137

Keyword

sign

Author

Seiichi Manyama, May 18 2022

Status

approved