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A130746
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A triangular sequence related to Binomial[n+2,3]/ A000292 and Binomial[n+1,2]/ A000217 as a sequence of Binomials.
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0
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1, 1, 4, 1, 5, 15, 1, 6, 21, 56, 1, 7, 28, 84, 210, 1, 8, 36, 120, 330, 792, 1, 9, 45, 165, 495, 1287, 3003, 1, 10, 55, 220, 715, 2002, 5005, 11440, 1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 1, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sum is A002054: Table[Sum[Binomial[n + i, i + 1], {n, 1, i}], {i, 1, 10}] {1, 5, 21, 84, 330, 1287, 5005, 19448, 75582, 293930}
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FORMULA
| a(n,m) = Binomial[n+m,1+m]
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EXAMPLE
| {1},
{1, 4},
{1, 5, 15},
{1, 6, 21, 56},
{1, 7, 28, 84, 210},
{1, 8, 36, 120, 330, 792},
{1, 9, 45, 165, 495, 1287, 3003},
{1, 10, 55, 220, 715, 2002, 5005, 11440}
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MATHEMATICA
| Table[Table[Binomial[n + i, i + 1], {n, 1, i}], {i, 1, 10}] Flatten[%]
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CROSSREFS
| Cf. A002054, A000292, A000217.
Sequence in context: A100279 A132379 A193955 * A125078 A087841 A194576
Adjacent sequences: A130743 A130744 A130745 * A130747 A130748 A130749
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 12 2007
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