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Search: id:A100327
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| A100327 |
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Row sums of triangle A100326, in which row n equals the inverse binomial of column n of square array A100324. |
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+0
4
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| 1, 2, 8, 42, 252, 1636, 11188, 79386, 579020, 4314300, 32697920, 251284292, 1953579240, 15336931928, 121416356108, 968187827834, 7769449728780, 62696580696172, 508451657412496, 4141712433518956, 33872033298518728
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Self-convolution yields A100328, which equals column 1 of triangle A100326 (omitting leading zero).
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FORMULA
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G.f. A(x) = (1+G003169(x))/(1-G003169(x)), also A(x)^2 = (1+G003169(x))*G003169(x), where G003169(x) is the g.f. of A003169. a(0)=1, a(n) = 2*A003168(n) for n>0; a(n) = Sum_{k=1..n} 2*binomial(n, k)*binomial(2n+k, k-1)/n for n>0.
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PROGRAM
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(PARI) a(n)=if(n==0, 1, sum(k=0, n, 2*binomial(n, k)*binomial(2*n+k, k-1)/n))
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CROSSREFS
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Cf. A003168, A003169, A100326.
Sequence in context: A129277 A120916 A133417 this_sequence A018934 A107588 A013999
Adjacent sequences: A100324 A100325 A100326 this_sequence A100328 A100329 A100330
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 17 2004
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