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A154230
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A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n*(n + 1)*(2*n + 1)*(3*n^2 + 3*n - 1)/30)*A(n - 2, k - 1).
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1, 1, 1, 1, 100, 1, 1, 455, 455, 1, 1, 1435, 98810, 1435, 1, 1, 3711, 1135370, 1135370, 3711, 1, 1, 8388, 7849141, 464306300, 7849141, 8388, 1, 1, 17161, 40410421, 10431621081, 10431621081, 40410421, 17161, 1, 1, 32495, 169040786
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 102, 912, 101682, 2278164, 480021360, 20944097328, 7402055707536,
545380929025296,...}.
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n*(n + 1)*(2*n + 1)*(3*n^2 + 3*n - 1)/30)**A(n - 2, k - 1).
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EXAMPLE
| {1},
{1, 1},
{1, 100, 1},
{1, 455, 455, 1},
{1, 1435, 98810, 1435, 1},
{1, 3711, 1135370, 1135370, 3711, 1},
{1, 8388, 7849141, 464306300, 7849141, 8388, 1},
{1, 17161, 40410421, 10431621081, 10431621081, 40410421, 17161, 1},
{1, 32495, 169040786, 130822910455, 7140071740062, 130822910455, 169040786, 32495, 1},
{1, 57829, 603812894, 1154709146434, 271535151495490, 271535151495490, 1154709146434, 603812894, 57829, 1}
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MATHEMATICA
| A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n*(n + 1)*(2*n + 1)*(3*n^2 + 3*n - 1)/30)*A[n - 2, k - 1];
Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A093211 A010114 A015068 * A173183 A172179 A147804
Adjacent sequences: A154227 A154228 A154229 * A154231 A154232 A154233
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 05 2009
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