A316593 a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 3 + 1/x^m)^m for n >= 1.

1, 6, 30, 145, 685, 3267, 15533, 74338, 356284, 1714020, 8263596, 39940398, 193419915, 938440188, 4560542645, 22196008209, 108171753355, 527816934216, 2578310320610, 12607506013260, 61706212041096, 302275147959675, 1481908332595625, 7270432038855843, 35694090764454926, 175351391301452028, 861946790726717742, 4239292356515821416, 20860889073855326397, 102703447427882985153

Offset

1,2

Comments

The coefficient of 1/x^n in Sum_{m>=0} (x^m + 3 + 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) * 3^k for n >= 1.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..300

Formula

a(n) ~ 5^(n + 1/2) / (2*sqrt(Pi*n)). - Vaclav Kotesovec, Jul 10 2018

Example

G.f.: A(x) = x + 6*x^2 + 30*x^3 + 145*x^4 + 685*x^5 + 3267*x^6 + 15533*x^7 + 74338*x^8 + 356284*x^9 + 1714020*x^10 + 8263596*x^11 + 39940398*x^12 + ...
such that Sum_{m>=0} (x^m + 3 + 1/x^m)^m = A(x) + A(1/x) + (infinity)*x^0.

Prog

(PARI) {a(n) = polcoeff( sum(m=1, n, (x^-m + 3 + x^m)^m +x*O(x^n)), n, x)}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

Cf. A304638, A316590, A316591, A316592, A316594, A316595.

Sequence in context: A046945 A216045 A307494 * A089817 A364460 A006320

Adjacent sequences: A316590 A316591 A316592 * A316594 A316595 A316596

Keyword

nonn

Author

Paul D. Hanna, Jul 08 2018

Status

approved