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Search: id:A141689
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| 1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 36, 15, 1, 1, 31, 156, 156, 31, 1, 1, 63, 603, 1218, 603, 63, 1, 1, 127, 2157, 7827, 7827, 2157, 127, 1, 1, 255, 7318, 44145, 78130, 44145, 7318, 255, 1, 1, 511, 23938, 227638, 655240, 655240, 227638, 23938, 511, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are: {1, 2, 5, 16, 68, 376, 2552, 20224, 181568, 1814656, ...}.
If Pascal's triangle and the Eulerian numbers are both fundamental arrays, then there should be a combinatorial set "between" them.
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EXAMPLE
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{1},
{1, 1},
{1, 3, 1},
{1, 7, 7, 1},
{1, 15, 36, 15, 1},
{1, 31, 156, 156, 31, 1},
{1, 63, 603, 1218, 603, 63, 1},
{1, 127, 2157, 7827, 7827, 2157, 127, 1},
{1, 255, 7318, 44145, 78130, 44145, 7318, 255, 1},
{1, 511, 23938, 227638, 655240, 655240, 227638, 23938, 511, 1}
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MATHEMATICA
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Table[Table[(Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] + Binomial[n - 1, k])/2, {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Cf. A008292, A007318.
Sequence in context: A136126 A046802 A022166 this_sequence A058669 A057004 A059328
Adjacent sequences: A141686 A141687 A141688 this_sequence A141690 A141691 A141692
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 13 2008
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