OFFSET
0,3
FORMULA
If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).
From Seiichi Manyama, Dec 01 2024: (Start)
G.f.: exp( Sum_{k>=1} A378567(k) * x^k/k ).
a(n) = (1/(n+1)) * [x^n] 1/(1 - x/(1 - x)^4)^(n+1).
G.f.: (1/x) * Series_Reversion( x*(1 - x/(1 - x)^4) ). (End)
PROG
(PARI) a(n, s=4, t=2, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 11 2023
STATUS
approved