A009410 E.g.f. log(1+x)*cos(x).

0, 1, -1, -1, 0, 9, -45, 279, -2072, 17265, -160065, 1638031, -18353544, 223578809, -2943054205, 41639195623, -630238419600, 10162622387809, -173942578536993, 3149754003442847, -60163773962649200, 1208991988527548137

Offset

0,6

Links

Robert Israel, Table of n, a(n) for n = 0..450

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * cos(1). - Vaclav Kotesovec, Jan 23 2015

a(n) = -i*n*(i^n*3F1(1,1,1-n;2;-i)-(-i)^n*3F1(1,1,1-n;2;i))/2, n>0. - Benedict W. J. Irwin, May 30 2016

(4*(n+4))*(n+3)*(n+2)*(n+1)*a(n)+(16*(n+4))*(n+3)*(n+2)*a(n+1)+(n+4)*(n+3)*(8*n^2+32*n+51)*a(n+2)+(2*(n+4))*(16*n^2+92*n+135)*a(n+3)+(4*n^4+48*n^3+254*n^2+722*n+869)*a(n+4)+(4*(4*n^3+42*n^2+151*n+189))*a(n+5)+(n+4)*(23*n+89)*a(n+6)+(2*(7*n+30))*a(n+7)+3*a(n+8) = 0. - Robert Israel, May 30 2016

Recurrence: (4*n^2 - 32*n + 67)*a(n) = -2*(4*n^3 - 40*n^2 + 131*n - 138)*a(n-1) - (n-4)*(4*n^3 - 36*n^2 + 115*n - 139)*a(n-2) - 4*(n-3)*(4*n^2 - 30*n + 57)*a(n-3) - (2*n - 9)*(4*n^3 - 38*n^2 + 124*n - 141)*a(n-4) - 2*(n-4)*(4*n^2 - 28*n + 51)*a(n-5) - (n-5)*(n-4)*(4*n^2 - 24*n + 39)*a(n-6). - Vaclav Kotesovec, May 30 2016

a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^(n-k-1) * binomial(n,2*k) * (n-2*k-1)!. - Ilya Gutkovskiy, Apr 10 2022

Maple

S:= series(log(1+x)*cos(x), x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, May 30 2016

Mathematica

CoefficientList[Series[Cos[x]*Log[1 + x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
Table[- I n (I^n HypergeometricPFQ[{1, 1, 1 - n}, {2}, -I] - (-I)^n HypergeometricPFQ[{1, 1, 1 - n}, {2}, I])/2, {n, 1, 20}] (* Benedict W. J. Irwin, May 30 2016 *)

Crossrefs

Cf. A009416.

Sequence in context: A026092 A054628 A132133 * A290358 A030113 A001556

Adjacent sequences: A009407 A009408 A009409 * A009411 A009412 A009413

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved