A368173 Expansion of e.g.f. -log(1 - x^2/2 * (exp(x) - 1)).

0, 0, 0, 3, 6, 10, 105, 651, 2968, 26496, 265905, 2203795, 22830456, 288661308, 3476579197, 44960585775, 671394654960, 10329701480416, 164573071219233, 2865785889662019, 52647629639499280, 1000194250108913580, 20125846165307543661, 426789766980101676943

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..454

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * Stirling2(n-2*k,k)/(2^k * (n-2*k)!).

a(0) = a(1) = a(2) = 0; a(n) = n*(n-1)/2 + Sum_{k=3..n-1} k*(k-1)/2 * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 22 2025

Prog

(PARI) a(n) = n!*sum(k=1, n\3, (k-1)!*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));

Crossrefs

Cf. A052858, A368174.

Cf. A353998.

Sequence in context: A350993 A308849 A354000 * A125567 A254957 A124266

Adjacent sequences: A368170 A368171 A368172 * A368174 A368175 A368176

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2023

Status

approved