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A367060
G.f. satisfies A(x) = 1 + x*A(x)^3 + x^3*A(x)^4.
5
1, 1, 3, 13, 62, 318, 1718, 9627, 55437, 326070, 1950630, 11831706, 72597453, 449804148, 2810260317, 17685019893, 111997074910, 713223954540, 4564502770117, 29341499243806, 189364923816282, 1226535071582818, 7970416067268898, 51949175133236526
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k+1,k) * binomial(3*n-5*k,n-3*k)/(2*n-2*k+1).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*n-2*k+1, k)*binomial(3*n-5*k, n-3*k)/(2*n-2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 04 2023
STATUS
approved