A366431 G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^(5/2).

1, 1, 5, 25, 135, 775, 4651, 28845, 183450, 1190050, 7844230, 52389678, 353770190, 2411324700, 16568343325, 114639216915, 798076174113, 5586035989185, 39287407321075, 277508001643575, 1967816928168265, 14003018984540741, 99965175670335750

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Partial sums give A366400.

Cf. A006319, A071724, A213282, A213336, A366432, A366433, A366434, A366435, A366436, A366437.

Sequence in context: A222570 A344268 A144818 * A048370 A272706 A275905

Adjacent sequences: A366428 A366429 A366430 * A366432 A366433 A366434

Keyword

nonn

Author

Seiichi Manyama, Oct 09 2023

Status

approved