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A098265
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G.f. : 1/(1-2x-23x^2)^(1/2).
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2
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1, 1, 13, 37, 289, 1201, 7741, 38053, 227137, 1207009, 6995053, 38591653, 221446369, 1245188881, 7130897437, 40516456357, 232260610177, 1327920945601, 7627285093069, 43787832627493, 252042452907169, 1451244932278129, 8370001674641917, 48303478743113893, 279083099450496961
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OFFSET
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0,3
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COMMENTS
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Central coefficient of (1+x+6x^2)^n.
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LINKS
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FORMULA
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E.g.f.: exp(x)*BesselI(0, 2*sqrt(6)x).
a(n) = sum{k=0..floor(n/2), binomial(n, k)*binomial(n-k, k)*6^k}.
a(n) = sum{k=0..floor(n/2), binomial(n, 2k)*binomial(2k, k)*6^k}.
n*a(n) +(1-2n)*a(n-1) +23(1-n)*a(n-2)=0. (Recurrence (4) in the Noe paper).- Veka Gesell, Jun 26 2012
a(n) ~ sqrt(72+6*sqrt(6))*(1+2*sqrt(6))^n/(12*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 14 2012
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MATHEMATICA
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Table[SeriesCoefficient[1/Sqrt[1-2*x-23*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
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PROG
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(PARI) x='x+O('x^66); Vec(1/(1-2*x-23*x^2)^(1/2)) \\ Joerg Arndt, May 11 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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