A009633 E.g.f. tan(cos(x)*x) (odd powers only).

1, -1, -39, 55, 39697, -2289, -235548247, -1367615353, 4617417380769, 85802560805023, -226896487004217095, -9332987296855749801, 23509703520941274769841, 1792438008018628579394735

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(n)=sum(k=0..n, binomial(2*n+1,2*k+1)*(sum(i=0..k,(2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i)))*(sum(j=1..2*k+1, j!*2^(1-j)*(-1)^(n+1+j)*stirling2(2*k+1,j)))). - Vladimir Kruchinin, Jun 18 2011

Mathematica

terms = 14;
egf = Tan[Cos[x]*x] + O[x]^(2 terms);
Partition[ CoefficientList[egf, x] Range[0, 2 terms - 1]!, 2][[All, 2]] (* Jean-François Alcover, Sep 24 2019 *)

Prog

(Maxima)
a(n):=sum(binomial(2*n+1, 2*k+1)*(sum((2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1, i), i, 0, k))*(sum(j!*2^(1-j)*(-1)^(n+1+j)*stirling2(2*k+1, j), j, 1, 2*k+1)), k, 0, n); /* Vladimir Kruchinin, Jun 18 2011 */

Crossrefs

Sequence in context: A268083 A063480 A305026 * A327586 A156333 A116281

Adjacent sequences: A009630 A009631 A009632 * A009634 A009635 A009636

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved