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A154229
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A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n*(n + 1)/2)^2*A(n - 2, k - 1).
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0
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1, 1, 1, 1, 38, 1, 1, 139, 139, 1, 1, 365, 8828, 365, 1, 1, 807, 70492, 70492, 807, 1, 1, 1592, 357459, 7062136, 357459, 1592, 1, 1, 2889, 1404923, 98777227, 98777227, 1404923, 2889, 1, 1, 4915, 4631612, 824036625, 14498379854, 824036625, 4631612
(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, 40, 280, 9560, 142600, 7780240, 200370080, 16155726160, 638430944320,...}.
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n*(n + 1)/2)^2*A(n - 2, k - 1).
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EXAMPLE
| {1},
{1, 1},
{1, 38, 1},
{1, 139, 139, 1},
{1, 365, 8828, 365, 1},
{1, 807, 70492, 70492, 807, 1},
{1, 1592, 357459, 7062136, 357459, 1592, 1},
{1, 2889, 1404923, 98777227, 98777227, 1404923, 2889, 1},
{1, 4915, 4631612, 824036625, 14498379854, 824036625, 4631612, 4915, 1},
{1, 7941, 13375752, 5078560312, 314123528154, 314123528154, 5078560312, 13375752, 7941, 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)^2*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: A171407 A023930 A022072 * A037936 A121672 A160147
Adjacent sequences: A154226 A154227 A154228 * A154230 A154231 A154232
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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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