A349021 G.f. satisfies A(x) = 1/(1 - x/(1 - x*A(x))^2)^4.

1, 4, 18, 104, 671, 4624, 33342, 248412, 1897219, 14774152, 116864936, 936390692, 7584216152, 61992689940, 510728310716, 4236545121924, 35354229533389, 296604036437692, 2500154435955614, 21164005790766980, 179841032283906149, 1533499916749203208

Offset: 0

Author

Seiichi Manyama, Nov 06 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006013, A109081, A161799.

Programs

Maple

A349021 := proc(n)
    local s,t ;
    s := 2 ;
    t := 4;
    add( binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k) /(n-k+1) ,k=0..n) ;
end proc:
seq(A349021(n),n=0..40) ; # R. J. Mathar, May 12 2022

PARI

a(n, s=2, 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).