A167435 Hankel transform of A084076.

1, 2, -16, -3584, -1114112, -771751936, -68719476736, 50102545854496768, 4999067643975288487936, 1104958199127771065681444864, 363815722265501838229553819942912

Offset: 0

Author

Paul Barry, Nov 03 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..50

Programs

Mathematica

a[n_] := Sum[Binomial[n + k, 2*k]*(-2)^(n - k), {k, 0, n}]; Table[2^(n^2)*(-1)^n*a[n], {n, 0, 10}] (* G. C. Greubel, Jun 13 2016 *)

Formula

a(n) = 2^(n^2)*(-1)^n*Sum_{k=0..n} C(n+k,2k)*(-2)^(n-k).

a(n) = 2^(n^2)*[x^n](1-2*x)/(1+3*x+4*x^2) = 2^(n^2) *A247560(n).