login
A367112
G.f. satisfies A(x) = 1 + 2*x*A(x) + x^3*A(x)^3.
3
1, 2, 4, 9, 24, 72, 227, 730, 2384, 7916, 26704, 91280, 315319, 1098710, 3856948, 13628441, 48435808, 173030048, 620965396, 2237681720, 8093572960, 29372735368, 106925552672, 390336084256, 1428620011263, 5241166583502, 19270575881964
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(n,3*k) * A001764(k).
PROG
(PARI) a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(n, 3*k)*binomial(3*k, k)/(2*k+1));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 05 2023
STATUS
approved