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A154227 A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + n*(n + 1)*A(n - 2, k - 1)/2. 0
1, 1, 1, 1, 8, 1, 1, 19, 19, 1, 1, 35, 158, 35, 1, 1, 57, 592, 592, 57, 1, 1, 86, 1629, 5608, 1629, 86, 1, 1, 123, 3767, 28549, 28549, 3767, 123, 1, 1, 169, 7760, 105621, 309458, 105621, 7760, 169, 1, 1, 225, 14694, 320566, 1985274, 1985274, 320566, 14694, 225 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 10, 40, 230, 1300, 9040, 64880, 536560, 4641520,...}.

LINKS

Table of n, a(n) for n=0..53.

FORMULA

A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + n*(n + 1)*A(n - 2, k - 1)/2.

EXAMPLE

{1},

{1, 1},

{1, 8, 1},

{1, 19, 19, 1},

{1, 35, 158, 35, 1},

{1, 57, 592, 592, 57, 1},

{1, 86, 1629, 5608, 1629, 86, 1},

{1, 123, 3767, 28549, 28549, 3767, 123, 1},

{1, 169, 7760, 105621, 309458, 105621, 7760, 169, 1},

{1, 225, 14694, 320566, 1985274, 1985274, 320566, 14694, 225, 1}

MATHEMATICA

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

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

Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A051425 A051469 A155494 * A166340 A157178 A174303

Adjacent sequences:  A154224 A154225 A154226 * A154228 A154229 A154230

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 05 2009

STATUS

approved

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Last modified September 19 15:09 EDT 2020. Contains 337178 sequences. (Running on oeis4.)