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A227667 Number of lattice paths from {n}^5 to {0}^5 using steps that decrement one component by 1 such that for each point (p_1,p_2,...,p_5) we have abs(p_{i}-p_{i+1}) <= 1. 2

%I

%S 1,120,29392,7453320,1897242448,482913033152,122911984813568,

%T 31283451053916800,7962224756951452544,2026535155335964884480,

%U 515791104488454210243072,131278484324109833244067840,33412829924638979294019463168,8504190228674549912505288509440

%N Number of lattice paths from {n}^5 to {0}^5 using steps that decrement one component by 1 such that for each point (p_1,p_2,...,p_5) we have abs(p_{i}-p_{i+1}) <= 1.

%H Alois P. Heinz, <a href="/A227667/b227667.txt">Table of n, a(n) for n = 0..200</a>

%F G.f.: (173568*x^8 -3773248*x^7 +10330944*x^6 -719888*x^5 +1468896*x^4 -35208*x^3 -3608*x^2 +170*x-1) / (-98304*x^9 +4024832*x^8 -36900032*x^7 +37771968*x^6 -3950640*x^5 +5084576*x^4 -23648*x^3 -9016*x^2 +290*x-1).

%e a(1) = 5! = 120.

%p a:= n-> coeff(series((173568*x^8 -3773248*x^7 +10330944*x^6 -719888*x^5 +1468896*x^4 -35208*x^3 -3608*x^2 +170*x-1) / (-98304*x^9 +4024832*x^8 -36900032*x^7 +37771968*x^6 -3950640*x^5 +5084576*x^4 -23648*x^3 -9016*x^2 +290*x-1), x, n+1), x, n): seq(a(n), n=0..20);

%Y Column k=5 of A227655.

%Y Cf. A000142.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jul 19 2013

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Last modified September 19 07:24 EDT 2020. Contains 337178 sequences. (Running on oeis4.)