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A157153 Triangle read by rows: A(n,0)=A(n,n)=0 and A(n,k)= (2*(n-k)+1)*A(n-1,k-1) + (2*k+1)*A(n-1,k) - 2*k*(n-k)*A(n-2,k-1) for 1<=k<n. 0
1, 1, 1, 1, 4, 1, 1, 13, 13, 1, 1, 40, 98, 40, 1, 1, 121, 614, 614, 121, 1, 1, 364, 3519, 6832, 3519, 364, 1, 1, 1093, 19179, 64759, 64759, 19179, 1093, 1, 1, 3280, 101368, 558712, 947038, 558712, 101368, 3280, 1, 1, 9841, 525436, 4538324, 12078814, 12078814 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are 1, 2, 6, 28, 180, 1472, 14600, 170064, 2273760, 34304832, 576383520,...

LINKS

Table of n, a(n) for n=0..50.

EXAMPLE

1;

1, 1;

1, 4, 1;

1, 13, 13, 1;

1, 40, 98, 40, 1;

1, 121, 614, 614, 121, 1;

1, 364, 3519, 6832, 3519, 364, 1;

1, 1093, 19179, 64759, 64759, 19179, 1093, 1;

1, 3280, 101368, 558712, 947038, 558712, 101368, 3280, 1;

1, 9841, 525436, 4538324, 12078814, 12078814, 4538324, 525436, 9841, 1;

1, 29524, 2689517, 35392352, 140889362, 218382008, 140889362, 35392352, 2689517, 29524, 1;

MATHEMATICA

Clear[A, n, k, m];

A[n_, 0, m_] := 1;

A[n_, n_, m_] := 1;

A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m* k + 1)*A[n - 1, k, m] - m*k*(n - k)*A[n - 2, k - 1, m];

Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];

Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]

CROSSREFS

Sequence in context: A255494 A146956 A152613 * A212801 A147565 A022167

Adjacent sequences:  A157150 A157151 A157152 * A157154 A157155 A157156

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 24 2009

STATUS

approved

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Last modified July 12 17:10 EDT 2020. Contains 335665 sequences. (Running on oeis4.)