OFFSET
0,5
COMMENTS
Hankel transform is A178079.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Paul Barry, Integer sequences from elliptic curves, arXiv:2306.05025 [math.NT], 2023.
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-2*k-i)*3^(n-2*k-i)*(-2)^i*1^(k-i) ).
MATHEMATICA
Table[Sum[(Binomial[n-k, k]/(n-2*k+1))*Sum[Binomial[k, j]*Binomial[n-k-j-1, n-2*k-j]*3^(n-2*k-j)*(-2)^j*1^(k-j), {j, 0, k}], {k, 0, Floor[n/2]}] + ((1 + (-1)^n)*(2/3)^(n/2))/2, {n, 0, 50}] (* 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)*3^(n-2*k-j)*(-2)^j));
for(n=0, 50, print1(a(n), ", ")) \\ G. C. Greubel, Sep 18 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 19 2010
STATUS
approved