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

0,4

Links

Table of n, a(n) for n=0..18.

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.

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 *)

Prog

(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));

Crossrefs

Sequence in context: A002961 A063071 A251963 * A160682 A097261 A158555

Adjacent sequences: A192004 A192005 A192006 * A192008 A192009 A192010

Keyword

sign

Author

Vladimir Kruchinin, Jun 21 2011

Status

approved