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A154228
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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)/6)*A(n - 2, k - 1).
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0
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1, 1, 1, 1, 16, 1, 1, 47, 47, 1, 1, 103, 974, 103, 1, 1, 195, 5354, 5354, 195, 1, 1, 336, 19969, 147068, 19969, 336, 1, 1, 541, 60085, 1259253, 1259253, 60085, 541, 1, 1, 827, 156386, 7010503, 44432886, 7010503, 156386, 827, 1, 1, 1213, 365498, 30299614
(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, 18, 96, 1182, 11100, 187680, 2639760, 58768320, 1133844240,...}.
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n*(n + 1)*(2*n + 1)/6)*A(n - 2, k - 1).
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EXAMPLE
| {1},
{1, 1},
{1, 16, 1},
{1, 47, 47, 1},
{1, 103, 974, 103, 1},
{1, 195, 5354, 5354, 195, 1},
{1, 336, 19969, 147068, 19969, 336, 1},
{1, 541, 60085, 1259253, 1259253, 60085, 541, 1},
{1, 827, 156386, 7010503, 44432886, 7010503, 156386, 827, 1},
{1, 1213, 365498, 30299614, 536255794, 536255794, 30299614, 365498, 1213, 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)/6)*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: A040257 A040256 A133824 * A141697 A202750 A177823
Adjacent sequences: A154225 A154226 A154227 * A154229 A154230 A154231
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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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