A367234 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^4.
1, 1, 6, 35, 226, 1561, 11276, 84150, 643730, 5021038, 39781858, 319282210, 2590312872, 21208628405, 175024439504, 1454329099044, 12157356271998, 102170610282040, 862721635191860, 7315768816166027, 62274763166575410, 531950072655682896, 4558282056420235664
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Keywords
Programs
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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));
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)