A009670 - OEIS

%I #18 Apr 02 2017 11:56:06

%S 1,-2,-48,880,59136,-4558336,-358510592,87349164032,5261729398784,

%T -4294386293800960,-9972473469599744,442881767885962739712,

%U -50940651947982996897792,-83250857495799899292172288

%N E.g.f. tan(sin(x)*cos(x)) (odd powers only).

%F a(n)=2*sum(m=0..n, 4^(n-m)*((sum(j=1..2*m+1, j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1, j)))*sum(i=0..(2*m+1)/2, (2*i-(2*m+1))^(2*n+1)*binomial(2*m+1, i)*(-1)^(n+1-i)))/(2*m+1)!). - _Vladimir Kruchinin_, Jun 29 2011

%o (Maxima)

%o a(n):=2*sum(4^(n-m)*((sum(j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1, j), j, 1, 2*m+1))*sum((2*i-(2*m+1))^(2*n+1)*binomial(2*m+1, i)*(-1)^(n+1-i), i, 0, (2*m+1)/2))/(2*m+1)!, m, 0, n); /* _Vladimir Kruchinin_, Jun 28 2011 */

%Y Cf. A101921.

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997