A375176 Expansion of e.g.f. exp( (exp( (exp(9*x) - 1)/3 ) - 1)/3 ).

1, 1, 13, 208, 4132, 99328, 2799073, 90310006, 3281661436, 132615087517, 5897867191525, 286140731152972, 15031839986716483, 849637058684740030, 51389339196926149645, 3310400979718767433801, 226189040323182011660827, 16333609964679285918346633

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(n) = Sum_{k=0..n} 9^(n-k) * Stirling2(n,k) * A004212(k) = 9^n * Sum_{k=0..n} (1/3)^k * Stirling2(n,k) * Bell_k(1/3), where Bell_n(x) is n-th Bell polynomial.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((exp((exp(9*x)-1)/3)-1)/3)))

Crossrefs

Cf. A374882, A375174.

Cf. A004212.

Sequence in context: A319115 A145270 A296671 * A196328 A362550 A340431

Adjacent sequences: A375173 A375174 A375175 * A375177 A375178 A375179

Keyword

nonn

Author

Seiichi Manyama, Aug 02 2024

Status

approved