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A156184 A generalized recursion triangle sequence : m=1; t(n,k)=(k + m - 1)*t(n - 1, k, m) + (m*n - k + 1 - m)*t(n - 1, k - 1, m). 0
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 16, 7, 1, 1, 11, 53, 53, 11, 1, 1, 16, 150, 318, 150, 16, 1, 1, 22, 380, 1554, 1554, 380, 22, 1, 1, 29, 892, 6562, 12432, 6562, 892, 29, 1, 1, 37, 1987, 25038, 82538, 82538, 25038, 1987, 37, 1, 1, 46, 4270, 89023, 480380, 825380, 480380 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:A054091;

{1, 2, 4, 10, 32, 130, 652, 3914, 27400, 219202, 1972820,...}.

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

Table of n, a(n) for n=0..61.

FORMULA

t(n,k)=(k + m - 1)*t(n - 1, k, m) + (m*n - k + 1 - m)*t(n - 1, k - 1, m).

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 4, 4, 1},

{1, 7, 16, 7, 1},

{1, 11, 53, 53, 11, 1},

{1, 16, 150, 318, 150, 16, 1},

{1, 22, 380, 1554, 1554, 380, 22, 1},

{1, 29, 892, 6562, 12432, 6562, 892, 29, 1},

{1, 37, 1987, 25038, 82538, 82538, 25038, 1987, 37, 1},

{1, 46, 4270, 89023, 480380, 825380, 480380, 89023, 4270, 46, 1}

MATHEMATICA

m = 1; 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}], {n, 0, 10}];

Flatten[%]

CROSSREFS

A054091, A054090, A008517, A156141

Sequence in context: A086629 A203948 A296990 * A056588 A126770 A202979

Adjacent sequences:  A156181 A156182 A156183 * A156185 A156186 A156187

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.)