A156188 - OEIS

A156188

Triangle: m=5; 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).

2, 1, 1, 1, 10, 1, 1, 80, 80, 1, 1, 775, 1520, 775, 1, 1, 10915, 25945, 25945, 10915, 1, 1, 213720, 542910, 624670, 542910, 213720, 1, 1, 5245530, 14690640, 16408670, 16408670, 14690640, 5245530, 1, 1, 151534685, 479956020, 553630850, 464654480

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..40.

FORMULA

m=5; 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, 10, 1},

{1, 80, 80, 1},

{1, 775, 1520, 775, 1},

{1, 10915, 25945, 25945, 10915, 1},

{1, 213720, 542910, 624670, 542910, 213720, 1},

{1, 5245530, 14690640, 16408670, 16408670, 14690640, 5245530, 1},...

MATHEMATICA

m = 5; 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

Cf. A054091, A054090, A008517, A156141.

Sequence in context: A288972 A065521 A225700 * A179930 A007737 A229243

Adjacent sequences: A156185 A156186 A156187 * A156189 A156190 A156191

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 05 2009

STATUS

approved