A002969 E.g.f. 1/(1 - sin(x) + sin(x)^2).

1, 1, 0, -7, -24, 61, 1200, 4493, -48384, -781319, -1804800, 85444193, 1210361856, -1847527499, -288162201600, -3428482320907, 33720680349696, 1637781983297521, 14158399925452800, -431041350297034807, -14236987086964260864

Offset

0,4

Links

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

Formula

a(n) = 2*sum(m=1..n, sum(j=0..(n-m)/2, (binomial(m,n-m-2*j)*sum(i=0..(n-2*j)/2, (2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(m-j-i)))/2^(n-2*j))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 08 2011

Mathematica

With[{nn=20}, CoefficientList[Series[1/(1-Sin[x]+Sin[x]^2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 20 2015 *)

Prog

(Maxima)
a(n):=2*sum(sum((binomial(m, n-m-2*j)*sum((2*i+2*j-n)^n*binomial(n-2*j, i)*(-1)^(m-j-i), i, 0, (n-2*j)/2))/2^(n-2*j), j, 0, (n-m)/2), m, 1, n); /* Vladimir Kruchinin, Jun 08 2011 */

Crossrefs

Cf. A029585.

Sequence in context: A008779 A062449 A014205 * A029585 A114291 A211382

Adjacent sequences: A002966 A002967 A002968 * A002970 A002971 A002972

Keyword

sign

Author

N. J. A. Sloane

Status

approved