A366034 G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*(1 - x)^3*A(x)^3.

1, 4, 15, 70, 405, 2676, 19075, 142562, 1100961, 8711968, 70257055, 575269278, 4769615773, 39961571228, 337805166747, 2877506096794, 24675158973081, 212835736433304, 1845348003175063, 16073746202176150, 140590118902532757, 1234285061013293716

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A014140, A164965, A366215.

Cf. A366184.

Sequence in context: A098614 A367040 A356407 * A027316 A085349 A185133

Adjacent sequences: A366031 A366032 A366033 * A366035 A366036 A366037

Keyword

nonn

Author

Seiichi Manyama, Oct 04 2023

Status

approved