A009563 E.g.f. sin(x/cosh(x)) (odd powers only).

1, -4, 56, -1688, 84160, -6141312, 613282944, -80158806016, 13267800137728, -2710082835353600, 669033814167273472, -196220826200422416384, 67398310755666413387776, -26784943833122921085534208

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..238

Formula

a(n) = 2*Sum_{m=0..n-1} binomial(2*n+1,2*m+1)*(Sum_{j=0..(n-m)} binomial(m+j-1/2,j)*4^(n-m-j)*Sum_{i=0..j} (i-j)^(2*n-2*m)* binomial(2*j,i)*(-1)^(m+j-i))) + (-1)^n. - Vladimir Kruchinin, Jun 16 2011

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sin[x/Cosh[x]], {x, 0, nn}], x] Range[ 0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Dec 24 2017 *)

Prog

(Maxima) a(n):=2*sum(binomial(2*n+1, 2*m+1)*(sum(binomial(m+j-1/2, j)*4^(n-m-j)*sum((i-j)^(2*n-2*m)*binomial(2*j, i)*(-1)^(m+j-i), i, 0, j), j, 0, (n-m))), m, 0, n-1)+(-1)^n; /* Vladimir Kruchinin, Jun 16 2011 */
(PARI) my(x='x+O('x^50)); v=Vec(serlaplace(sin(x/cosh(x)))); vector((#v-1)\2 , n, v[2*n-1]) \\ G. C. Greubel, Jan 21 2018

Crossrefs

Sequence in context: A009558 A113583 A174489 * A261747 A111849 A009159

Adjacent sequences: A009560 A009561 A009562 * A009564 A009565 A009566

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved