A349024 G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^3.
1, 3, 18, 124, 951, 7764, 66200, 582594, 5252133, 48254668, 450186720, 4253328540, 40612877001, 391300954065, 3799506069816, 37142836241690, 365255937037437, 3610755090793272, 35861607622930556, 357670540310182842, 3580797575489620740
Offset: 0
Keywords
Programs
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PARI
a(n, s=4, t=3) = 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).