A349022 G.f. satisfies A(x) = 1/(1 - x/(1 - x*A(x))^3)^4.

1, 4, 22, 152, 1161, 9460, 80550, 708172, 6379368, 58576168, 546215580, 5158542152, 49239812893, 474285453628, 4604149947276, 44999181550032, 442430807369519, 4372944634271688, 43425156714959956, 433049078716727332, 4334925824762251939

Offset: 0

Author

Seiichi Manyama, Nov 06 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..972

Crossrefs

Cf. A006632, A161797, A161798.

Programs

Maple

A349022 := proc(n)
    add(binomial(4*n-3*(k-1),k)*binomial(n+2*k-1,n-k)/(n-k+1),k=0..n) ;
end proc:
seq(A349022(n),n=0..40) ; # R. J. Mathar, Jan 25 2023

PARI

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

Formula

If g.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).