A009210 Expansion of e.g.f.: exp(sin(x)*cos(x)).

1, 1, 1, -3, -15, -23, 177, 1253, 1057, -37103, -245471, 371085, 15691665, 76436089, -608056239, -10302629131, -20287425215, 856245051169, 8821231566145, -29959421725155, -1376333505095631, -7591883371988471, 139148719952772849

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..125

Formula

a(n) = Sum_{j=0..(n-1)/2} 2^(4*j-n+1)*(Sum_{i=0..(n-2*j)/2} (2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(n-j-i))/(n-2*j)!, n>0, a(0)=1. - Vladimir Kruchinin, May 29 2011

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * (-4)^k * a(n-2*k-1). - Ilya Gutkovskiy, Feb 24 2022

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[Sin[x]*Cos[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 10 2021 *)

Prog

(Maxima)
a(n):=sum((2^(4*j-n+1)*sum((2*i+2*j-n)^n*binomial(n-2*j, i)*(-1)^(n-j-i), i, 0, ((n-2*j)/2)))/(n-2*j)!, j, 0, ((n-1)/2)); /* Vladimir Kruchinin, May 29 2011 */
(PARI) x='x+O('x^66); Vec(serlaplace(exp(sin(x)*cos(x)))) /* Joerg Arndt, May 29 2011 */

Crossrefs

Sequence in context: A060649 A344073 A366956 * A142882 A161467 A101133

Adjacent sequences: A009207 A009208 A009209 * A009211 A009212 A009213

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition corrected by Joerg Arndt, May 29 2011

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Aug 10 2021

Status

approved