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.

1, 120, 29392, 7453320, 1897242448, 482913033152, 122911984813568, 31283451053916800, 7962224756951452544, 2026535155335964884480, 515791104488454210243072, 131278484324109833244067840, 33412829924638979294019463168, 8504190228674549912505288509440

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

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).

Example

a(1) = 5! = 120.

Maple

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);

Crossrefs

Column k=5 of A227655.

Cf. A000142.

Sequence in context: A151604 A104008 A278726 * A054778 A230729 A027493

Adjacent sequences: A227664 A227665 A227666 * A227668 A227669 A227670

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 19 2013

Status

approved