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 A208616 Number of Young tableaux with 3 n-length rows, increasing entries down the columns and monotonic entries along the rows (first row increasing). 2
 1, 1, 10, 53, 491, 6091, 87781, 1386529, 23374495, 414325055, 7646034683, 145862292213, 2861143072425, 57468095412921, 1178095930854841, 24584089994286121, 521086299342539671, 11198784502153759831, 243661974373753909051, 5360563436205104422681 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of (3*n-1)-step walks on n-dimensional cubic lattice from (1,0,...,0) to (3,3,...,3) with positive unit steps in all dimensions such that for each point (p_1,p_2,...,p_n) we have p_1<=p_2<=...<=p_n or p_1>=p_2>=...>=p_n. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..220 MAPLE a:= proc(n) option remember; `if`(n<5, [1, 1, 10, 53, 491][n+1],       ((116013096898*n^6 -1106227006064*n^5 +3651730072724*n^4       -5019246600372*n^3 +2923780805838*n^2 -701199942904*n) *a(n-1)       +(-429126244301*n^6 +4283495440027*n^5 -14793057372915*n^4       +19089754215809*n^3 -168467698444*n^2 -17547244920336*n       +9564646580160) *a(n-2) +(24700698282*n^6 +2323122442728*n^5       -31157649402714*n^4 +153639646198428*n^3 -363480023453028*n^2       +415894667210784*n -184360926114960) *a(n-3) +(292122384552*n^6       -5522876986500*n^5 +42303228071580*n^4 -167574646102140*n^3       +360649174254588*n^2 -397826818736400*n +174796279534800) *a(n-4))/       (n*(3709935431*n^5 -22486109809*n^4 +4251368675*n^3 +135507711725*n^2       -75536091046*n -180596388856)))     end: seq (a(n), n=0..30); CROSSREFS Row n=3 of A208615. Sequence in context: A006889 A007035 A093187 * A219169 A152762 A161458 Adjacent sequences:  A208613 A208614 A208615 * A208617 A208618 A208619 KEYWORD nonn,walk AUTHOR Alois P. Heinz, Feb 29 2012 STATUS approved

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