OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..314
FORMULA
G.f.: Sum_{n>=0} (1+x)^(4*n^2) /(1 + (1+x)^(4*n))^(n+1).
a(n) ~ c * d^n * n! / sqrt(n), where d = 4*A317855 = 12.64435461546171525532068881035252996690553109675422536650911283015078823687... and c = 0.31492557816516652573983016205911709623053... - Vaclav Kotesovec, Aug 09 2018
EXAMPLE
G.f.: A(x) = 1 + 4*x + 70*x^2 + 2180*x^3 + 95729*x^4 + 5422192*x^5 + 375951144*x^6 + 30833206304*x^7 + ...
such that
A(x) = 1 + ((1+x)^4-1) + ((1+x)^8-1)^2 + ((1+x)^12-1)^3 + ((1+x)^16-1)^4 + ((1+x)^20-1)^5 + ((1+x)^24-1)^6 + ((1+x)^28-1)^7 + ...
Also,
A(x) = 1/2 + (1+x)^4/(1 + (1+x)^4)^2 + (1+x)^16/(1 + (1+x)^8)^3 + (1+x)^36/(1 + (1+x)^12)^4 + (1+x)^64/(1 + (1+x)^16)^5 + (1+x)^100/(1 + (1+x)^20)^6 + ...
PROG
(PARI) {a(n) = my(A, o=x*O(x^n)); A = sum(m=0, n, ((1+x +o)^(4*m) - 1)^m ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 24 2018
STATUS
approved