A366698 -id:A366698 - cp's OEIS frontend

A366699 G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^4.

1, 4, 19, 173, 1860, 21814, 271388, 3515330, 46906860, 640321565, 8899950644, 125524292790, 1791943900656, 25843064347685, 375956017001280, 5510454405453368, 81297696816798684, 1206334991431968912, 17991734573723974384, 269560224872407933010

Offset: 0

Seiichi Manyama, Oct 16 2023

nonn

Cf. A366267, A366698, A366700.

Cf. A364624.

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

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

A366700 G.f. satisfies A(x) = (1 + x)^4 + x*A(x)^4.

Original entry on oeis.org

1, 5, 26, 258, 3093, 40333, 558368, 8051416, 119614784, 1818190754, 28142073936, 442026009500, 7027713442496, 112879991541322, 1828959159551328, 29857735697705720, 490633308020085056, 8108894353260093213, 134705809490320133544

Offset: 0

Seiichi Manyama, Oct 16 2023

nonn

Cf. A366267, A366698, A366699.

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

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

cp's OEIS Frontend

A366699 G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^4.

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