OFFSET
0,7
COMMENTS
Compare to: 1+x = Sum_{n>=0} x^n * (1+x)^(n*(n-1)/2) / G(x)^(n*(n+1)/2) holds when G(x) = (1+x).
EXAMPLE
G.f.: A(x) = 1 + x^2 + x^4 + x^5 + 3*x^6 + 10*x^7 + 31*x^8 + 121*x^9 + 464*x^10 + 1944*x^11 + 8454*x^12 + 38468*x^13 + 182126*x^14 + 893488*x^15 + ...
such that
1/(1-x) = 1 + x/A(x) + x^2*(1+x)/A(x)^3 + x^3*(1+x)^3/A(x)^6 + x^4*(1+x)^6/A(x)^10 + x^5*(1+x)^10/A(x)^15 + x^6*(1+x)^15/A(x)^21 + x^7*(1+x)^21/A(x)^28 + x^8*(1+x)^28/A(x)^36 + x^9*(1+x)^36/A(x)^45 + ...
PROG
(PARI) a(n)=my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff(sum(m=0, #A, x^m*((1+x+x*O(x^#A))^(m*(m-1)/2)/Ser(A)^(m*(m+1)/2)-1)), #A)); A[n+1]
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 01 2019
STATUS
approved