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Search: id:A146990
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| A146990 |
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Symmetrically shifted Pascal triangle: t(n,m)=If[n < 2, Binomial[n, m], Binomial[n, m] + n^(n - 1)*Binomial[n - 2, m - 1]]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 68, 134, 68, 1, 1, 630, 1885, 1885, 630, 1, 1, 7782, 31119, 46676, 31119, 7782, 1, 1, 117656, 588266, 1176525, 1176525, 588266, 117656, 1, 1, 2097160, 12582940, 31457336, 41943110, 31457336, 12582940, 2097160, 1, 1
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:{1, 2, 6, 26, 272, 5032, 124480, 3764896, 134217984, 5509980800, 256000001024}.
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FORMULA
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t(n,m)=If[n < 2, Binomial[n, m], Binomial[n, m] + n^(n - 1)*Binomial[n - 2, m - 1]].
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EXAMPLE
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{1}, {1, 1}, {1, 4, 1}, {1, 12, 12, 1}, {1, 68, 134, 68, 1}, {1, 630, 1885, 1885, 630, 1}, {1, 7782, 31119, 46676, 31119, 7782, 1}, {1, 117656, 588266, 1176525, 1176525, 588266, 117656, 1}, {1, 2097160, 12582940, 31457336, 41943110, 31457336, 12582940, 2097160, 1}, {1, 43046730, 301327083, 903981225, 1506635361, 1506635361, 903981225, 301327083, 43046730, 1}, {1, 1000000010, 8000000045, 28000000120, 56000000210, 70000000252, 56000000210, 28000000120, 8000000045, 1000000010, 1}
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MATHEMATICA
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Table[If[n <2, Binomial[n, m], Binomial[n, m] + n^(n - 1)*Binomial[n - 2, m - 1]], {n, 0, 10}, {m, 0, n}]; Flatten[%]
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CROSSREFS
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A028262
Adjacent sequences: A146987 A146988 A146989 this_sequence A146991 A146992 A146993
Sequence in context: A099759 A072590 A111636 this_sequence A051433 A140070 A101275
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 04 2008
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