A378732 G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)) )^4.
1, 4, 10, 36, 155, 704, 3384, 16844, 86097, 449344, 2384170, 12822556, 69743953, 382982940, 2120323014, 11822279232, 66327376437, 374162700460, 2120999728610, 12075668658000, 69021358842795, 395909382981572, 2278286453089574, 13149207655326372, 76096242994616990
Offset: 0
Keywords
Programs
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PARI
a(n, r=4, s=1, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Formula
G.f.: A(x) = (1 + x*B(x))^4 where B(x) is the g.f. of A364743.
If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).