OFFSET
0,9
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
EXAMPLE
G.f.: A(x) = 1 + x + x^3 + x^5 + x^6 + 4*x^8 + 6*x^10 + 13*x^11 + 9*x^12 + 48*x^13 + 101*x^14 + 147*x^15 + 542*x^16 + 1244*x^17 + 2385*x^18 + 8158*x^19 + 19191*x^20 + ...
such that
1 = 1/A(x) + x/(1-x)/A(x)^3 + x^2/(1-x)^3/A(x)^6 + x^3/(1-x)^6/A(x)^10 + x^4/(1-x)^10/A(x)^15 + x^5/(1-x)^15/A(x)^21 + x^6/(1-x)^21/A(x)^28 + x^7/(1-x)^28/A(x)^36 + ...
Compare to the trivial identity:
1 = 1/(1+x) + x*(1+x)/(1+x)^3 + x^2*(1+x)^3/(1+x)^6 + x^3*(1+x)^6/(1+x)^10 + x^4*(1+x)^10/(1+x)^15 + x^5*(1+x)^15/(1+x)^21 + ...
PROG
(PARI) {a(n) = my(A=[1], V); for(i=0, n, A = concat(A, 0); V = Vec(sum(n=0, #A, 1/(1-x +x*O(x^#A))^(n*(n+1)/2)*x^n/Ser(A)^((n+1)*(n+2)/2)) ); A[#A]=V[#A] ); A[n+1]}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 24 2018
STATUS
approved