A009217 E.g.f. exp(sin(x)^2) (even powers only).

1, 2, 4, -88, -1136, 46112, 1098304, -103251328, -1963486976, 585781985792, -5685626878976, -6083058037577728, 447306486332821504, 87514624808197824512, -19369074730552627675136

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

a(n)=2*sum(k=1..n, (sum(i=0..k, (2*i-2*k)^(2*n)*binomial(2*k,i)*(-1)^(n+k-i)))/(4^k*k!)). - Vladimir Kruchinin, Jun 01 2011

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Exp[Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Aug 25 2024 *)

Prog

(Maxima)
a(n):=2*sum((sum((2*i-2*k)^(2*n)*binomial(2*k, i)*(-1)^(n+k-i), i, 0, k))/(4^k*k!), k, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */

Crossrefs

Sequence in context: A121103 A018397 A259137 * A015170 A013146 A116310

Adjacent sequences: A009214 A009215 A009216 * A009218 A009219 A009220

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Aug 25 2024

Status

approved