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A157152 Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (n-k+1)*A(n-1,k-1) + (k+1)*A(n-1,k) - k*(n-k)*A(n-2,k-1) for 1<=k<n. 0
1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 30, 15, 1, 1, 31, 108, 108, 31, 1, 1, 63, 359, 594, 359, 63, 1, 1, 127, 1145, 2875, 2875, 1145, 127, 1, 1, 255, 3568, 12985, 19246, 12985, 3568, 255, 1, 1, 511, 10966, 56306, 116640, 116640, 56306, 10966, 511, 1, 1, 1023, 33417 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are 1, 2, 5, 16, 62, 280, 1440, 8296, 52864, 368848, 2794864,...

LINKS

Table of n, a(n) for n=0..57.

EXAMPLE

1;

1, 1;

1, 3, 1;

1, 7, 7, 1;

1, 15, 30, 15, 1;

1, 31, 108, 108, 31, 1;

1, 63, 359, 594, 359, 63, 1;

1, 127, 1145, 2875, 2875, 1145, 127, 1;

1, 255, 3568, 12985, 19246, 12985, 3568, 255, 1;

1, 511, 10966, 56306, 116640, 116640, 56306, 10966, 511, 1;

1, 1023, 33417, 238024, 665702, 918530, 665702, 238024, 33417, 1023, 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: A063394 A193871 A108470 * A136126 A046802 A184173

Adjacent sequences:  A157149 A157150 A157151 * A157153 A157154 A157155

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 24 2009

STATUS

approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)