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A371608
G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^3) )^2.
0
1, 2, 3, 14, 55, 226, 1042, 4840, 23103, 113118, 561568, 2826550, 14392534, 73967650, 383271596, 2000096144, 10502029735, 55446004880, 294155761676, 1567371462762, 8384300275607, 45009106969022, 242400290365756, 1309314066314354, 7091306989205453
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(k,n-k)/(3*(n-k)+1).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137966.
PROG
(PARI) a(n, r=2, s=1, t=0, u=6) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
CROSSREFS
Sequence in context: A070207 A268559 A346057 * A270707 A141148 A275554
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 29 2024
STATUS
approved