A354136 Expansion of e.g.f. exp(log(1 + x)^3/6).

1, 0, 0, 1, -6, 35, -215, 1414, -9912, 73044, -552570, 4102626, -26654826, 79506492, 2154425364, -73527421176, 1708053626880, -35961691589640, 736338276883080, -15067241745943680, 312009998091705720, -6579362641255341120, 141704946709227843480

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-1,k-1) * Stirling1(k,3) * a(n-k).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(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-1, j-1)*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*k!));

Crossrefs

Cf. A354137.

Cf. A327504, A347002, A354134.

Sequence in context: A144638 A291246 A117671 * A370323 A317409 A354324

Adjacent sequences: A354133 A354134 A354135 * A354137 A354138 A354139

Keyword

sign

Author

Seiichi Manyama, May 18 2022

Status

approved