A366178 -id:A366178 - cp's OEIS frontend

A366179 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x).

1, 3, 13, 80, 582, 4627, 38906, 340138, 3060404, 28151835, 263546436, 2502686416, 24048985907, 233410500126, 2284790496700, 22530585455108, 223610524426654, 2231886642819974, 22389017726854323, 225604735477075272, 2282518274913713101

Offset: 0

Seiichi Manyama, Oct 03 2023

nonn

Partial sums of A366178.

Cf. A364620, A364629, A366180.

a(n) = sum(k=0, n, binomial(n+4*k+1, n-k)*binomial(3*k, k)/(2*k+1));

a(n) = Sum_{k=0..n} binomial(n+4*k+1,n-k) * binomial(3*k,k)/(2*k+1).

A366177 G.f. A(x) satisfies A(x) = 1/(1 - x) + x*A(x)^3/(1 - x)^2.

Original entry on oeis.org

1, 2, 9, 55, 382, 2866, 22648, 185722, 1565725, 13486036, 118163960, 1049908872, 9437623630, 85671158757, 784247925911, 7231502249005, 67106161264660, 626221543735984, 5872908642398977, 55323451127462123, 523240983692525619, 4966658879361416551

Offset: 0

Seiichi Manyama, Oct 03 2023

nonn

Partial sums give A364620.

Cf. A199475, A346626, A366178.

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

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

cp's OEIS Frontend

A366179 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x).

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