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A371678
G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x)^(1/2))^2.
4
1, 4, 56, 1068, 23504, 561972, 14183880, 371911132, 10031990560, 276589937892, 7759696110808, 220805824681740, 6357540660485616, 184876232243020564, 5422016433851400552, 160187931368799105468, 4763038761416835095616, 142426926824923660491716
OFFSET
0,2
FORMULA
G.f. satisfies A(x) = ( 1 + x * A(x)^3 * (1 + A(x)^(1/2)) )^2.
G.f.: B(x)^2 where B(x) is the g.f. of A371700.
a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(6*n+k+2,n)/(6*n+k+2).
PROG
(PARI) a(n, r=2, t=6, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 02 2024
STATUS
approved