A364621 -id:A364621 - cp's OEIS frontend

A364620 G.f. satisfies A(x) = 1/(1-x)^2 + x*A(x)^3.

1, 3, 12, 67, 449, 3315, 25963, 211685, 1777410, 15263446, 133427406, 1183336278, 10620959908, 96292118665, 880540044576, 8112042293581, 75218203558241, 701439747294225, 6574348389693202, 61897799517155325, 585138783209680944, 5551797662571097495

Offset: 0

Seiichi Manyama, Jul 30 2023

nonn

Cf. A086616, A364621.

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

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

A366698 G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^4.

Original entry on oeis.org

1, 3, 13, 106, 1000, 10315, 112732, 1282262, 15021212, 179994093, 2195807684, 27179964798, 340514877488, 4309512389582, 55014793453124, 707582318505678, 9160219144520568, 119268621622902920, 1560830776582842660, 20519083242145870778, 270851956372499374728

Offset: 0

Seiichi Manyama, Oct 16 2023

nonn

Cf. A366267, A366699, A366700.

Cf. A364621.

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

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

cp's OEIS Frontend

A364620 G.f. satisfies A(x) = 1/(1-x)^2 + x*A(x)^3.

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