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 A156186 A generalized recursion triangle sequence : m=3; e(n,k,n)=(k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m); t(n,k)=e(n,k,m)+e(n,n-k,m). 0
 2, 1, 1, 1, 6, 1, 1, 30, 30, 1, 1, 159, 360, 159, 1, 1, 1119, 3639, 3639, 1119, 1, 1, 10932, 41262, 57414, 41262, 10932, 1, 1, 136764, 582642, 898632, 898632, 582642, 136764, 1, 1, 2031933, 9957168, 16634718, 17182152, 16634718, 9957168, 2031933, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are: {2, 8, 62, 680, 9518, 161804, 3236078, 74429792, 1935174590, 56120063108,...}. The sequence comes from a generalization of the recurrence for A008517. REFERENCES Weisstein, Eric W. "Second-Order Eulerian Triangle." http://mathworld.wolfram.com/Second-OrderEulerianTriangle.html LINKS FORMULA m=3; e(n,k,n)=(k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m); t(n,k)=e(n,k,m)+e(n,n-k,m). EXAMPLE {2}, {1, 1}, {1, 6, 1}, {1, 30, 30, 1}, {1, 159, 360, 159, 1}, {1, 1119, 3639, 3639, 1119, 1}, {1, 10932, 41262, 57414, 41262, 10932, 1}, {1, 136764, 582642, 898632, 898632, 582642, 136764, 1}, {1, 2031933, 9957168, 16634718, 17182152, 16634718, 9957168, 2031933, 1}, {1, 34474173, 194894781, 369132246, 369086094, 369086094, 369132246, 194894781, 34474173, 1}, {1, 654773346, 4228768422, 9285005715, 9780535908, 8221896324, 9780535908, 9285005715, 4228768422, 654773346, 1} MATHEMATICA m = 3; e[n_, 0, m_] := 1; e[n_, k_, m_] := 0 /; k >= n; e[n_, k_, 1] := 1 /; k >= n; e[n_, k_, m_] := (k + m - 1)e[n - 1, k, m] + (m*n - k + 1 - m)e[n - 1, k - 1, m]; Table[Table[e[n, k, m], {k, 0, n - 1}], {n, 1, 10}]; Table[Table[e[n, k, m] + e[n, n - k, m], {k, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A320637 A280491 A157118 * A156233 A251725 A292977 Adjacent sequences:  A156183 A156184 A156185 * A156187 A156188 A156189 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 05 2009 STATUS approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)