A375175 Expansion of e.g.f. exp( (exp( (exp(4*x) - 1)/2 ) - 1)/2 ).

1, 1, 7, 63, 713, 9753, 156111, 2858103, 58845105, 1344371793, 33713484151, 919838859151, 27105053988793, 857310780134825, 28953291147179007, 1039373409620929671, 39505610599553955809, 1584411299793530257697, 66846625774893448843879

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * Stirling2(n,k) * A004211(k) = 4^n * Sum_{k=0..n} (1/2)^k * Stirling2(n,k) * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((exp((exp(4*x)-1)/2)-1)/2)))

Crossrefs

Cf. A080893, A375173.

Cf. A004211.

Sequence in context: A015684 A051579 A185106 * A275577 A049464 A229078

Adjacent sequences: A375172 A375173 A375174 * A375176 A375177 A375178

Keyword

nonn

Author

Seiichi Manyama, Aug 02 2024

Status

approved