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Search: id:A129824
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| A129824 |
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a(n) = Product from k=0 to k=n of 1 + C(n,k) so that a(0) = 2, where C(n,k) is the usual binomial coefficient. |
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+0
1
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| 2, 4, 64, 700, 17424, 1053696, 160579584, 61971036120
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OFFSET
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0,1
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COMMENT
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A product analog of the binomial expansion.
The sequence is a special case of a(n) = Product from k=0 to k=n of 1 + C(n,k)x^k.
Let C be a collection of subsets of an n-element set S. Then a(n) is the number of possible shapes K = (k_0, ..., k_n) of C, where k_i is the number of i-element subsets of S in C. - Gabriel Cunningham (oeis(AT)gabrielcunningham.com), Nov 08 2007
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REFERENCES
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H. W. Gould, A product analog of the binomial expansion, unpublished manuscript, Jun 03 2007.
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EXAMPLE
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a(4) = (1+1)(1+4)(1+6)(1+4)(1+1) = 2*5*7*5*2 = 700
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CROSSREFS
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Sequence in context: A009744 A124592 A088079 this_sequence A118993 A100603 A018364
Adjacent sequences: A129821 A129822 A129823 this_sequence A129825 A129826 A129827
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KEYWORD
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easy,nonn
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AUTHOR
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Henry W. Gould (gould(AT)math.wvu.edu), Jun 03 2007
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