OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..250
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 73*x^5 + 368*x^6 + 2074*x^7 + 12663*x^8 + 82236*x^9 + 561664*x^10 + 4004815*x^11 + 29662508*x^12 + ...
such that the following series are equal:
B(x) = 1 + x*A(x) + x^2*A(x)^3 + x^3*A(x)^6 + x^4*A(x)^10 + x^5*A(x)^15 + x^6*A(x)^21 + x^7*A(x)^28 + x^8*A(x)^36 + ...
B(x) = 1 + x/(1-x) + x^2/(1-x)^4 + x^3/(1-x)^9 + x^4/(1-x)^16 + x^5/(1-x)^25 + x^6/(1-x)^36 + x^7/(1-x)^49 + x^8/(1-x)^64 + ...
where
B(x) = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 83*x^5 + 363*x^6 + 1730*x^7 + 8889*x^8 + 48829*x^9 + 284858*x^10 + 1755325*x^11 + ... + A178325(n)*x^n + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = -polcoeff( sum(m=0, #A, x^m*( Ser(A)^(m*(m+1)/2) - 1/(1-x +x*O(x^#A))^(m^2)) ), #A) ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 25 2019
STATUS
approved