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Constant term in the expansion of (1 + v + w + x + y + z + 1/v + 1/w + 1/x + 1/y + 1/z)^n.
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%I #18 Oct 27 2019 02:26:24

%S 1,1,11,31,331,1451,15101,85961,876331,5917531,59415961,450749861,

%T 4481629021,36869221741,364723196891,3177413896031,31389891383531,

%U 284948206851691,2818704750978761,26367817118386661,261622144605718681,2502704635436220281,24932548891897186991

%N Constant term in the expansion of (1 + v + w + x + y + z + 1/v + 1/w + 1/x + 1/y + 1/z)^n.

%C a(n) is the number of n-step closed walks (from origin to origin) in 5-dimensional lattice where each step changes at most one component by -1 or by +1. - _Alois P. Heinz_, Oct 26 2019

%H Alois P. Heinz, <a href="/A328715/b328715.txt">Table of n, a(n) for n = 0..967</a>

%F E.g.f.: exp(x) * BesselI(0,2*x)^5. - _Ilya Gutkovskiy_, Oct 26 2019

%F From _Vaclav Kotesovec_, Oct 27 2019: (Start)

%F Recurrence: n^5*a(n) = (2*n - 1)*(n^2 - n + 1)*(3*n^2 - 3*n + 1)*a(n-1) + (n-1)*(125*n^4 - 500*n^3 + 903*n^2 - 806*n + 289)*a(n-2) - 2*(n-2)*(n-1)*(2*n - 3)*(135*n^2 - 405*n + 419)*a(n-3) - (n-3)*(n-2)*(n-1)*(3319*n^2 - 13276*n + 14637)*a(n-4) + 3867*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 5)*a(n-5) + 10395*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6).

%F a(n) ~ 11^(n + 5/2) / (32 * Pi^(5/2) * n^(5/2)). (End)

%o (PARI) {a(n) = polcoef(polcoef(polcoef(polcoef(polcoef((1+v+w+x+y+z+1/v+1/w+1/x+1/y+1/z)^n, 0), 0), 0), 0), 0)}

%Y Row 5 of A328718.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 26 2019

%E a(13)-a(22) from _Alois P. Heinz_, Oct 26 2019