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Search: id:A158690
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| A158690 |
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Expansion of the basic hypergeometric series 1 + (1-exp(-t)) + (1-exp(-t))*(1-exp(-3t)) + (1-exp(-t))*(1-exp(-3t))*(1-exp(-5t)) + ... as a series in t. |
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+0
6
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| 1, 1, 5, 55, 1073, 32671, 1431665, 85363615, 6646603073, 654896692351, 79656194515025, 11722538113191775, 2052949879753739873, 421931472111868912831, 100568330857984368195185
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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We appear to get the same sequence by expanding 1 - (1-exp(t)) + (1-exp(t))*(1-exp(2t)) - (1-exp(t))*(1-exp(2t))*(1-exp(3t)) + ... as a series in t. Compare with A079144. For other sequences with generating functions of a similar type see A000364, A000464, A002105 and A002439.
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FORMULA
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Basic hypergeometric generating function: 1 + Sum {n = 1..inf} Product {k = 1..n} (1-exp(2*k-1)*t)) = 1 + t + 5*t^2/2! + 55*t^3/3! + ....
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CROSSREFS
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A000364, A000464, A002105, A002439, A079144, A158691.
Sequence in context: A140049 A130031 A119399 this_sequence A102221 A056600 A126456
Adjacent sequences: A158687 A158688 A158689 this_sequence A158691 A158692 A158693
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Bala (pbala(AT)talktalk.net), Mar 24 2009
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