OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = G(G(x)-1), A(G(x)-1) = G(A(x)-1), A(x) = G(x*A(x)^5) and A(x/G(x)^5) = G(x), where G(x) is the g.f. of A120976 and satisfies G(x/G(x)^5) = 1 + x.
From Seiichi Manyama, Mar 01 2025: (Start)
Let a(n,k) = [x^n] A(x)^k.
a(n,0) = 0^n; a(n,k) = k * Sum_{j=0..n} binomial(5*n+k,j)/(5*n+k) * a(n-j,5*j). (End)
PROG
(PARI) {a(n)=local(A, G=[1, 1]); for(i=1, n, G=concat(G, 0); G[ #G]=-Vec(subst(Ser(G), x, x/Ser(G)^5))[ #G]); A=Vec(((Ser(G)-1)/x)^(1/5)); A[n+1]}
(PARI) a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(5*n+k, j)/(5*n+k)*a(n-j, 5*j))); \\ Seiichi Manyama, Mar 01 2025
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Paul D. Hanna, Jul 20 2006
STATUS
approved