OFFSET
1,2
COMMENTS
The coefficient of 1/x^n in Sum_{m>=0} (x^m + 4 + 1/x^m)^m equals a(n) for n > 0, while the constant term in the sum increases without limit.
a(n) = Sum_{k=0..n-1} A316590(n,k) * 4^k for n >= 1.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..260
FORMULA
a(n) ~ 2^(n - 1/2) * 3^(n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 10 2018
EXAMPLE
G.f.: A(x) = x + 8*x^2 + 51*x^3 + 305*x^4 + 1770*x^5 + 10236*x^6 + 58947*x^7 + 340164*x^8 + 1964863*x^9 + 11374720*x^10 + ...
such that Sum_{m>=0} (x^m + 4 + 1/x^m)^m = A(x) + A(1/x) + (infinity)*x^0.
PROG
(PARI) {a(n) = polcoeff( sum(m=1, n, (x^-m + 4 + x^m)^m +x*O(x^n)), n, x)}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 08 2018
STATUS
approved