A318793 Constant term in the expansion of (Sum_{k=0..n} k*(x^k + x^(-k)))^n.

1, 0, 10, 84, 12060, 922680, 203474180, 45546045720, 16977056982648, 7385901628225968, 4359210462435545640, 3063111491275816418020, 2669859570203387710219500, 2738752987417403052110951664, 3328615281192062743163487239944

Offset: 0

Author

Seiichi Manyama, Dec 15 2018

Keywords

• nonn

Examples

			(2/x^2 + 1/x + 0 + x + 2*x^2)^2 = 4/x^4 + 4/x^3 + 1/x^2 + 4/x + 10 + 4*x + x^2 + 4*x^3 + 4*x^4. So a(2) = 10.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..214

Crossrefs

Cf. A286928, A318794.

Programs

Mathematica

a[n_] := If[n==0, 1, Coefficient[Expand[Sum[k*(x^k + x^(-k)), {k, 0, n}]^n], x, 0]]; Array[a, 15, 0] (* Amiram Eldar, Dec 15 2018 *)

PARI

{a(n) = polcoeff((sum(k=0, n, k*(x^k+x^(-k))))^n, 0, x)}

Formula

a(n) ~ exp(1) * n^(2*n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Dec 15 2018