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

%I

%S 1,1,0,-7,-24,61,1200,4493,-48384,-781319,-1804800,85444193,

%T 1210361856,-1847527499,-288162201600,-3428482320907,33720680349696,

%U 1637781983297521,14158399925452800,-431041350297034807,-14236987086964260864

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

%F 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

%t 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 *)

%o (Maxima)

%o 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 */

%Y Cf. A029585.

%K sign

%O 0,4

%A _N. J. A. Sloane_

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)