A192007 E.g.f. sin(cos(x)-1) (even part).

0, -1, 1, 14, -209, 1259, 30856, -1561561, 37411921, -16085146, -60657859289, 4261856902379, -162682375304624, -1611913152464161, 993012713177088241, -109110124618216328866, 6878613768612426116431, 18035860168898476567739, -82542057452137913017262504

Offset: 0

Author

Vladimir Kruchinin, Jun 21 2011

Keywords

• sign

Programs

Mathematica

With[{nn=40},Take[CoefficientList[Series[Sin[Cos[x]-1],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Oct 10 2023 *)

Maxima

a(n):=if n=0 then 0 else 2*(sum(((-1)^(k)*sum(((sum((j-2*i)^(2*n)*binomial(j,i),i,0,(j-1)/2))*binomial(2*k+1,j)*(-1)^(n+1-j))/2^j,j,1,2*k+1))/(2*k+1)!,k,0,n));

Formula

a(n)=2*(sum(k=0..n, ((-1)^(k)*sum(j=1..2*k+1,((sum(i=0..(j-1)/2, (j-2*i)^(2*n)*binomial(j,i)))*binomial(2*k+1,j)*(-1)^(n+1-j))/2^j))/(2*k+1)!)), n>0, a(0)=0.