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Search: id:A104455
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| A104455 |
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Expansion of exp(5x)*(BesselI(0,2x)-BesselI(1,2x)). |
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+0
7
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| 1, 4, 17, 77, 371, 1890, 10095, 56040, 320795, 1881524, 11250827, 68330773, 420314629, 2612922694, 16389162537, 103587298965, 659071002195, 4217699773140, 27129590096595, 175303621195647, 1137400502295081
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Third binomial transform of A000108. In general, the k-th binomial transform of A000108 will have g.f. (1-sqrt((1-(k+4)x)/(1-kx)))/(2x), e.g.f. exp((k+2)x)(BesselI(0,2x)-BesselI(1,2x)) and a(n)=sum{i=0..n, C(n,i)C(i)k^(n-i)}.
Hankel transform of this sequence gives A000012 = [1,1,1,1,1,1,1,...] . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 24 2007
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FORMULA
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G.f.: (1-sqrt((1-7x)/(1-3x)))/(2x); a(n)=sum{k=0..n, C(n, k)C(k)3^(n-k)}.
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CROSSREFS
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Cf. A007317, A064613.
Sequence in context: A081922 A124325 A151248 this_sequence A123952 A005494 A053486
Adjacent sequences: A104452 A104453 A104454 this_sequence A104456 A104457 A104458
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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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