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A098663
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Sum k=0..n, binomial(n,k)binomial(n+1,k+1)3^k.
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1
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1, 5, 30, 193, 1286, 8754, 60460, 421985, 2968902, 21019510, 149572292, 1068795930, 7664092060, 55121602436, 397464604440, 2872406652001, 20799171328070, 150869330458830, 1096046132412628, 7973709600124958
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fourth binomial transform of A098662.
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FORMULA
| G.f.: ((1+2x)-sqrt(1-8x+4x^2))/(6xsqrt(1-8x+4x^2)); E.g.f.: exp(4x)(BesselI(0, 2sqrt(3)x)+BesselI(1, 2sqrt(3)x)/sqrt(3)).
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MATHEMATICA
| Table[Sum[Binomial[n, k]Binomial[n+1, k+1]3^k, {k, 0, n}], {n, 0, 20}] (* From Harvey P. Dale, Nov 08 2011 *)
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CROSSREFS
| Sequence in context: A006773 A059273 A038744 * A158828 A196471 A034164
Adjacent sequences: A098660 A098661 A098662 * A098664 A098665 A098666
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 20 2004
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