A009468 Expansion of sin(log(1+x)^2).

0, 0, 2, -6, 22, -100, 428, -1008, -12504, 325152, -5509368, 85326120, -1301444520, 20069047440, -316157970000, 5106165734880, -84530527771200, 1430269752307200, -24598613333889120, 426082994004863520, -7316749927773684000

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = sum(k=0..(n-1)/2, ((-1)^k*(4*k+2)!*stirling1(n,4*k+2))/(2*k+1)!). - Vladimir Kruchinin, Jun 28 2011

Example

sin(log(x+1)^2) = 2/2!*x^2-6/3!*x^3+22/4!*x^4-100/5!*x^5...

Mathematica

With[{nn=20}, CoefficientList[Series[Sin[Log[1+x]^2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 05 2023 *)

Prog

(Maxima)
a(n):=sum(((-1)^k*(4*k+2)!*stirling1(n, 4*k+2))/(2*k+1)!, k, 0, ((n-1)/2)); /* Vladimir Kruchinin, Jun 28 2011 */

Crossrefs

Sequence in context: A009789 A012271 A012266 * A088819 A177478 A376694

Adjacent sequences: A009465 A009466 A009467 * A009469 A009470 A009471

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Jul 05 2023

Status

approved