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Search: id:A104454
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| A104454 |
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Expansion of 1/(sqrt(1-5x)sqrt(1-9x)). |
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1
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| 1, 7, 51, 385, 2995, 23877, 194109, 1602447, 13389075, 112935445, 959783881, 8206116387, 70507643101, 608271899515, 5265458413875, 45711784088145, 397829544860115, 3469772959954245, 30319709631711225, 265383615634224675
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Fifth binomial transform of A000984. In general, the k-th binomial transform of A000984 will have g.f. 1/(sqrt(1-kx)sqrt(1-(k+4)x)) and a(n)=sum{i=0..n, C(n,i)C(2i,i)k^(n-i)}.
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REFERENCES
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Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
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G.f.: 1/sqrt(1-14x+45x^2); E.g.f.: exp(7x)BesselI(0, 2x) a(n)=sum{k=0..n, C(n, k)C(2k, k)5^(n-k)}.
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CROSSREFS
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Cf. A081671, A098409, A098410.
Adjacent sequences: A104451 A104452 A104453 this_sequence A104455 A104456 A104457
Sequence in context: A137382 A162757 A147958 this_sequence A019472 A081216 A124271
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 08 2005
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