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Search: id:A112492
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| A112492 |
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Triangle from inverse scaled Pochhammer symbols. |
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+0
10
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| 1, 1, 1, 1, 3, 1, 1, 7, 11, 1, 1, 15, 85, 50, 1, 1, 31, 575, 1660, 274, 1, 1, 63, 3661, 46760, 48076, 1764, 1, 1, 127, 22631, 1217776, 6998824, 1942416, 13068, 1, 1, 255, 137845, 30480800, 929081776, 1744835904, 104587344, 109584, 1, 1, 511, 833375
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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This expansion is based on the partial fraction identity: 1/product(x+j,j=1..m)= (1 + sum(((-1)^j)*binomial(m,j)*x/(x+j),j=1..m))/m!, e.g., p. 37 of the Ch. Jordan reference.
Another version of this triangle (without a column of 1's) is A008969.
The column sequences are, for m=1..10: A000012 (powers of 1), A000225, A001240, A001241, A001242, A111886-A111888.
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REFERENCES
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Charles Jordan, Calculus of Finite Differences, Chelsea, 1965.
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LINKS
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W. Lang, First 10 rows.
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FORMULA
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G.f. for column m>=1: (x^m)/product(1-m!*x/j, j=1..m).
a(n, m)= -(m!^(n-m+1))*sum(((-1)^j)*binomial(m, j)/j^(n-m+1), j=1..m), m>=1. a(n, m)=0 if n+1<m.
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CROSSREFS
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Row sums give A111885.
Sequence in context: A059328 A075440 A137470 this_sequence A049290 A134567 A131932
Adjacent sequences: A112489 A112490 A112491 this_sequence A112493 A112494 A112495
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 12 2005
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