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 A227580 Number of lattice paths from {n}^3 to {0}^3 using steps that decrement one component such that for each point (p_1,p_2,p_3) we have p_1<=p_2<=p_3. 2
 1, 1, 14, 290, 7680, 238636, 8285506, 312077474, 12509563082, 526701471002, 23076216957520, 1044813920439200, 48630132961189400, 2317337976558074760, 112689430179458971738, 5577655817793682738378, 280392321290875174774106, 14290804691034216155457274 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) ~ 2^(6*n+10)/(sqrt(3)*Pi*(5*n)^4). - Vaclav Kotesovec, Jul 18 2013 EXAMPLE a(2) = 14: [(2,2,2),(0,2,2),(0,0,2),(0,0,0)], [(2,2,2),(0,2,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,0)], [(2,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(0,2,2),(0,1,2),(0,1,1),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,0,2),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,1,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(0,2,2),(0,1,2),(0,1,1),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(0,1,2),(0,0,2),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(0,1,2),(0,0,2),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(0,1,2),(0,1,1),(0,0,1),(0,0,0)], [(2,2,2),(1,2,2),(1,1,2),(1,1,1),(0,1,1),(0,0,1),(0,0,0)]. MAPLE a:= proc(n) option remember; `if`(n<3, [1, 1, 14][n+1],       ((n+1)*(665*n^3-1433*n^2+980*n-204) *a(n-1)        -(n-2)*(1615*n^3-3218*n^2+1521*n-342) *a(n-2)        +192*(5*n-1)*(n-3)*(n-2)^2 *a(n-3)) /        (2*(n+2)*(5*n-6)*(n+1)^2))     end: seq(a(n), n=0..30); CROSSREFS Column k=3 of A227578. Sequence in context: A259432 A233069 A181192 * A215869 A262740 A158475 Adjacent sequences:  A227577 A227578 A227579 * A227581 A227582 A227583 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 16 2013 STATUS approved

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Last modified September 18 14:00 EDT 2018. Contains 315131 sequences. (Running on oeis4.)