A361705 Constant term in the expansion of (1 + w^4 + x^4 + y^4 + z^4 + 1/(w*x*y*z))^n.
1, 1, 1, 1, 1, 1, 1, 1, 1681, 15121, 75601, 277201, 831601, 2162161, 5045041, 10810801, 54054001, 592191601, 5035670641, 31553973361, 157346607601, 660308770801, 2420415874801, 7951853614321, 24853781309281, 91246800876001, 497098157556001, 3346262924004001
Offset: 0
Programs
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Mathematica
Table[Sum[(4*k)!/k!^4 * Binomial[8*k,4*k] * Binomial[n,8*k], {k,0,n/8}], {n,0,30}] (* Vaclav Kotesovec, Mar 25 2023 *) -
PARI
a(n) = sum(k=0, n\8, (4*k)!/k!^4*binomial(8*k, 4*k)*binomial(n, 8*k));
Formula
a(n) = Sum_{k=0..floor(n/8)} (4*k)!/k!^4 * binomial(8*k,4*k) * binomial(n,8*k).
a(n) ~ 5^(n+2) / (2^(5/2) * Pi^2 * n^2). - Vaclav Kotesovec, Mar 25 2023