A366239 -id:A366239 - cp's OEIS frontend

A366240 G.f. A(x) satisfies A(x) = 1 + x + x(1 + x)^3A(x)^3.

1, 2, 9, 60, 432, 3378, 27792, 237122, 2079132, 18620709, 169614960, 1566540573, 14635978998, 138080055192, 1313596636812, 12587218990644, 121378106852988, 1176981533610012, 11469587139406515, 112265849283068877, 1103256200355696855

Offset: 0

Seiichi Manyama, Oct 05 2023

nonn

Cf. A364336, A366239, A366241.

a(n) = sum(k=0, n, binomial(5*k+1, n-k)*binomial(3*k, k)/(2*k+1));

a(n) = Sum_{k=0..n} binomial(5*k+1,n-k) * binomial(3*k,k)/(2*k+1).

A366241 G.f. A(x) satisfies A(x) = 1 + x + x(1 + x)^4A(x)^3.

Original entry on oeis.org

1, 2, 10, 72, 552, 4593, 40185, 364413, 3395217, 32305005, 312589540, 3066565720, 30430287693, 304907935707, 3080617021926, 31349533179726, 321038696185371, 3305935381202847, 34211612434972446, 355605873560512974, 3710978684625678870

Offset: 0

Seiichi Manyama, Oct 05 2023

nonn

Cf. A364336, A366239, A366240.

Cf. A366222.

a(n) = sum(k=0, n, binomial(6*k+1, n-k)*binomial(3*k, k)/(2*k+1));

a(n) = Sum_{k=0..n} binomial(6*k+1,n-k) * binomial(3*k,k)/(2*k+1).

cp's OEIS Frontend

A366240 G.f. A(x) satisfies A(x) = 1 + x + x(1 + x)^3A(x)^3.

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A366241 G.f. A(x) satisfies A(x) = 1 + x + x(1 + x)^4A(x)^3.

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cp's OEIS Frontend

A366240 G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^3*A(x)^3.

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A366241 G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^4*A(x)^3.

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PARI

Formula

A366240 G.f. A(x) satisfies A(x) = 1 + x + x(1 + x)^3A(x)^3.

A366241 G.f. A(x) satisfies A(x) = 1 + x + x(1 + x)^4A(x)^3.