OFFSET
0,4
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
FORMULA
G.f. A(x) satisfies:
(1) 1 = Sum_{n>=0} x^n * (1+x)^(n*(n+1)*(n+2)/6) / A(x)^(n+1).
(2) 1 + x = Sum_{n>=0} x^n * (1+x)^(n*(n^2-1)/6) / A(x)^n.
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 6*x^4 + 25*x^5 + 127*x^6 + 768*x^7 + 5336*x^8 + 41830*x^9 + 365564*x^10 + 3523994*x^11 + 37211298*x^12 + ...
such that
1 = 1/A(x) + x*(1+x)/A(x)^2 + x^2*(1+x)^4/A(x)^3 + x^3*(1+x)^10/A(x)^4 + x^4*(1+x)^20/A(x)^5 + x^5*(1+x)^35/A(x)^6 + x^6*(1+x)^56/A(x)^7 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = Vec(sum(n=0, #A, (1+x +x*O(x^#A))^(n*(n+1)*(n+2)/6) * x^n/Ser(A)^n ) )[#A] ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 16 2019
STATUS
approved