A367880 Expansion of e.g.f. 1/(1 - 2 * x * (exp(x) - 1)).

1, 0, 4, 6, 104, 490, 7452, 65534, 1062224, 13825746, 252414020, 4303920742, 89701635960, 1870259792570, 44391086228972, 1085906907998670, 29112549152845472, 813723252665063842, 24402507959486170260, 765358519469125339190, 25431406241731942771400, 883304321080000124400522

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = 2 * n * Sum_{k=2..n} binomial(n-1,k-1) * a(n-k).

a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * k! * Stirling2(n-k,k)/(n-k)!.

Mathematica

terms = 21; CoefficientList[Series[1/(1 - 2 * x * (Exp[x] - 1)), {x, 0, terms}], x]*Range[0, terms]! (* Stefano Spezia, Dec 09 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, 2^k*k!*stirling(n-k, k, 2)/(n-k)!);

Crossrefs

Cf. A052848, A367881.

Sequence in context: A213128 A105037 A139730 * A013023 A012909 A219507

Adjacent sequences: A367877 A367878 A367879 * A367881 A367882 A367883

Keyword

nonn

Author

Seiichi Manyama, Dec 03 2023

Extensions

a(20)-a(21) from Stefano Spezia, Dec 09 2025

Status

approved