OFFSET
0,3
COMMENTS
Hankel transform is A178077.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/2)} ( (C(n-k,k)/(n-2k+1))*Sum_{i=0..k} C(k,i)*C(n-k-i-1,n-2k-i)*(-2)^(n-2k-i)*2^i*2^(k-i) ).
MATHEMATICA
Table[If[n == 0, 1, Sum[(Binomial[n-k, k]/(n-2*k+1))* Sum[Binomial[k, j]*Binomial[n-k-j-1, n-2*k-j]*(-2)^(n-2*k-j)*2^k, {j, 0, k}], {k, 0, Floor[n/2]}] + (1 + (-1)^n)/2], {n, 0, 100}] (* G. C. Greubel, Sep 18 2018 *)
PROG
(PARI) a(n) = sum(k=0, floor(n/2), sum(j=0, k, (binomial(n-k, k)/(n-2*k+1)) *binomial(k, j)*binomial(n-k-j-1, n-2*k-j)*(-2)^(n-2*k-j)*2^k));
for(n=0, 30, print1(a(n), ", ")) \\ G. C. Greubel, Sep 18 2018
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 19 2010
STATUS
approved