A367474 Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^2.

1, 4, 28, 272, 3360, 50256, 881616, 17734944, 402278496, 10155145344, 282329361024, 8570500876032, 282047266728192, 10001430040080384, 380152962804068352, 15418451851593596928, 664633482628021493760, 30342827915683778027520

Offset: 0

Author

Seiichi Manyama, Nov 19 2023

Keywords

• nonn

Crossrefs

Cf. A088500, A367475.

Cf. A052801, A367470.

Programs

PARI

a(n) = sum(k=0, n, 2^k*(k+1)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} 2^k * (k+1)! * |Stirling1(n,k)|.

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