A318793 - OEIS

%I #17 Dec 15 2018 07:26:47

%S 1,0,10,84,12060,922680,203474180,45546045720,16977056982648,

%T 7385901628225968,4359210462435545640,3063111491275816418020,

%U 2669859570203387710219500,2738752987417403052110951664,3328615281192062743163487239944

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

%H Vaclav Kotesovec, <a href="/A318793/b318793.txt">Table of n, a(n) for n = 0..214</a>

%F a(n) ~ exp(1) * n^(2*n - 3/2) / sqrt(Pi). - _Vaclav Kotesovec_, Dec 15 2018

%e (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.

%t 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 *)

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

%Y Cf. A286928, A318794.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 15 2018