A375990 Expansion of e.g.f. (1 + 2 * log(1 - x))^2.

1, -4, 4, 16, 64, 304, 1712, 11232, 84384, 715392, 6761088, 70513920, 804683520, 9975536640, 133513989120, 1919012014080, 29482606540800, 482183099596800, 8364495012249600, 153406409645260800, 2965940772905779200, 60291976261386240000

Offset: 0

Author

Seiichi Manyama, Sep 05 2024

Keywords

• sign
• easy

Crossrefs

Cf. A088500, A367474, A375945, A375953, A375987.

Cf. A182541.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[(1+2Log[1-x])^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 05 2025 *)

PARI

a(n) = if(n==0, 1, -4*(n-1)!+8*abs(stirling(n, 2, 1)));

Formula

a(n) = -4 * (n-1)! + 8 * |Stirling1(n,2)| for n > 0.