OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(2*k) = (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2, a(2*k+1) = (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), k >= 0.
a(n) = A054336(n+3, 3) (fourth column of convolution triangle). G.f.: (1/(1-x-x^2*c(x^2)))^4, with c(x) the g.f. for the Catalan numbers A000108.
G.f.: (c(x/(2x-1))/(1-2x))^4. - Michael Somos, Jul 31 2005
PROG
(PARI) {a(n)=local(k); if(n<0, 0, k=n\2; if(n%2, (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2 ))}
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wolfdieter Lang, Mar 27 2000
STATUS
approved