A368232 Expansion of e.g.f. 1/(1 - x - log(1 + x)).

1, 2, 7, 38, 272, 2444, 26306, 330588, 4746360, 76675584, 1376187072, 27171073632, 585216675600, 13655030234208, 343124183767920, 9237920561327904, 265292717180631552, 8094790891854169344, 261522698597072168832, 8918551194519088836864

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).

a(n) ~ n! * LambertW(exp(2)) / ((LambertW(exp(2)) + 1) * (LambertW(exp(2)) - 1)^(n+1)) . - Vaclav Kotesovec, Dec 29 2023

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A006252, A368233.

Cf. A338448.

Sequence in context: A168492 A346646 A032109 * A337026 A088792 A114160

Adjacent sequences: A368229 A368230 A368231 * A368233 A368234 A368235

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2023

Status

approved