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A099045
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a(n) = (3*0^n + 4^n*binomial(2*n,n))/4.
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4
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1, 2, 24, 320, 4480, 64512, 946176, 14057472, 210862080, 3186360320, 48432676864, 739699064832, 11342052327424, 174493112729600, 2692179453542400, 41639042214789120, 645405154329231360, 10022762396642181120, 155909637281100595200
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OFFSET
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0,2
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COMMENTS
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(1 + (k-1)*sqrt(1-4*k*x))/(k*sqrt(1-4*k*x)) is the g.f. for ((k-1)*0^n + k^n*binomial(2*n,n))/k.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..800
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FORMULA
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G.f.: (1+3*sqrt(1-16*x))/(4*sqrt(1-16*x)).
n*a(n) +8*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 24 2012
E.g.f.: (3 + exp(8*x) * BesselI(0,8*x)) / 4. - Ilya Gutkovskiy, Nov 17 2021
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MATHEMATICA
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Join[{1}, Table[4^(n-1)*Binomial[2*n, n], {n, 1, 30}]] (* G. C. Greubel, Dec 31 2017 *)
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PROG
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(MAGMA) [(3*0^n + 4^n*Binomial(2*n, n))/4: n in [ 0..20]]; // Vincenzo Librandi, Nov 24 2012
(PARI) for(n=0, 30, print1((3*0^n + 4^n*binomial(2*n, n))/4, ", ")) \\ G. C. Greubel, Dec 31 2017
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CROSSREFS
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Cf. A069723, A088218, A099044, A099046.
Sequence in context: A246610 A119491 A001864 * A181174 A209290 A333715
Adjacent sequences: A099042 A099043 A099044 * A099046 A099047 A099048
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Sep 24 2004
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STATUS
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approved
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