A368319 Expansion of e.g.f. exp(2*x) / (3 - 2*exp(x)).

1, 4, 22, 166, 1642, 20254, 299722, 5174446, 102094042, 2266154014, 55890234922, 1516265078926, 44874837768442, 1438774580904574, 49678366226498122, 1837828899444250606, 72522300447277154842, 3040654011774599283934, 134985159308312666889322

Offset

0,2

Links

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

Formula

a(n) = 2^n + 2 * Sum_{k=1..n} binomial(n,k) * a(n-k).

a(n) = (9/4)*A004123(n+1) - (1/2)*(1 + (3/2)*0^n).

Prog

(PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=2, t=2) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);

Crossrefs

Cf. A004123, A201339, A368320, A368321.

Sequence in context: A121397 A067369 A247249 * A113351 A001827 A363115

Adjacent sequences: A368316 A368317 A368318 * A368320 A368321 A368322

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2023

Status

approved