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A316594 a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 4 + 1/x^m)^m for n >= 1. 8
1, 8, 51, 305, 1770, 10236, 58947, 340164, 1964863, 11374720, 65966318, 383294335, 2230877428, 13005068804, 75923905800, 443837524793, 2597761611894, 15221637661064, 89283411393018, 524194446429830, 3080311943556785, 18115458477472312, 106618075368243534, 627937320952669230, 3700709501165664301, 21823188287212298688, 128765319930166601616, 760171656002439325155, 4489959180983688448616, 26532501571577231904204 (list; graph; refs; listen; history; text; internal format)
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

Cf. A304638, A316590, A316591, A316592, A316593, A316595.

Sequence in context: A295348 A082135 A153594 * A037697 A037606 A055147

Adjacent sequences:  A316591 A316592 A316593 * A316595 A316596 A316597

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 08 2018

STATUS

approved

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)