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Search: id:A098520
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| A098520 |
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E.g.f. exp(x)BesselI(1,4x)/2. |
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+0
1
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| 0, 1, 2, 15, 52, 285, 1206, 6027, 27560, 134073, 633130, 3062279, 14676828, 71045845, 343195230, 1665555075, 8084777040, 39343835505, 191627687250, 934855945215, 4565076327300, 22318461756045, 109211684822790
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of e.g.f. BesselI(1,4x)/2, or {0,1,0,12,0,160,0,2240,0,32256,0,...} with g.f. 2x/(1-16x^2+sqrt(1-16x^2)). The binomial transform of e.g.f. BesselI(1,2sqrt(r)x)/sqrt(r) with g.f. 2x/(1-(2sqrt(r)x)^2+sqrt(1-(2sqrt(r)x)^2)) has g.f. 2x/(1-2x-((2sqrt(r))^2-1)x^2+(1-x)sqrt(1-2x-((2sqrt(r))^2-1)x^2)).
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FORMULA
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G.f.: 2x/(1-2x-15x^2+(1-x)sqrt(1-2x-15x^2)); a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k+1)4^k}.
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CROSSREFS
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Sequence in context: A073877 A007972 A015520 this_sequence A056078 A088979 A034571
Adjacent sequences: A098517 A098518 A098519 this_sequence A098521 A098522 A098523
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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), Sep 12 2004
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