A350305 - OEIS

%I #19 Jan 15 2023 15:10:04

%S 1,1,13,1437,1884211,24657701475,3111336932350947,

%T 3710920324904591897521,41323213770479673319301068309,

%U 4261037235228828189774620497534270303,4045313784246510024420372971256850718016451185

%N a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^n.

%C a(n) is the coefficient of x^(n^2 * (n+1)/2) in Product_{k=0..n} (1 + x^k + x^(2*k))^n.

%H Robert Israel, <a href="/A350305/b350305.txt">Table of n, a(n) for n = 0..44</a>

%p f:= n -> coeff(mul(x^k+1+1/x^k,k=1..n)^n,x,0):

%p map(f, [$0..12]); # _Robert Israel_, Jan 15 2023

%t a[n_] := Coefficient[Series[Product[(x^k + 1 + 1/x^k)^n, {k, 1, n}], {x, 0, 0}], x, 0]; Array[a, 11, 0] (* _Amiram Eldar_, Dec 24 2021 *)

%o (PARI) a(n) = polcoef(prod(k=1, n, x^k+1+1/x^k)^n, 0);

%o (PARI) a(n) = polcoef(prod(k=1, n, 1+x^k+x^(2*k))^n, n^2*(n+1)/2);

%Y Cf. A007576, A156181, A225602, A350282, A350306, A350307.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 23 2021