A092785 a(n) = sum(sum(binomial(j-n-1,m),m=0..n),j=0..n).

1, -1, 7, -21, 81, -295, 1107, -4165, 15793, -60171, 230253, -884235, 3406105, -13154947, 50922987, -197519941, 767502945, -2987013067, 11641557717, -45429853651, 177490745985, -694175171647, 2717578296117, -10648297329691, 41757352712481, -163875286898935

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

Differs from A072547 by -1, +1, -1, +1, -1, ... - Ralf Stephan, Apr 19 2004

Equals sum(m=0, n, (-1)^m*binomial(n+m, m)). - Henry Gould, Apr 23 2004

Let f(n) = (-1)^n a(n). Then 2f(n) + f(n-1) = (3n+1)C(n) + (-1)^n, where C(n) = (2n+1)!/n!(n+1)! is a Catalan number (A000108). - Henry Gould, Apr 24 2004

Recurrence: 2*(n+1)*(15*n^2 - 31*n + 12)*a(n) = -(5*n-3)*(15*n^2 - 19*n - 4)*a(n-1) + (165*n^3 - 266*n^2 - 11*n + 60)*a(n-2) - 2*(2*n-3)*(15*n^2 - n - 4)*a(n-3). - Vaclav Kotesovec, Sep 05 2014

Crossrefs

Sequence in context: A241431 A147003 A110683 * A114902 A177369 A164544

Adjacent sequences: A092782 A092783 A092784 * A092786 A092787 A092788

Keyword

sign

Author

Francois Jooste (pin(AT)myway.com), Apr 23 2004

Status

approved