A099046 a(n) = (4*0^n + 5^n*binomial(2*n,n))/5.

1, 2, 30, 500, 8750, 157500, 2887500, 53625000, 1005468750, 18992187500, 360851562500, 6888984375000, 132038867187500, 2539208984375000, 48970458984375000, 946762207031250000, 18343517761230468750, 356080050659179687500, 6923778762817382812500

Offset

0,2

Comments

(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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..760

Formula

G.f.: (1 + 4*sqrt(1-20*x))/(5*sqrt(1-20*x)).

n*a(n) +10*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 24 2012

E.g.f.: (4 + exp(10*x) * BesselI(0,10*x)) / 5. - Ilya Gutkovskiy, Nov 17 2021

Mathematica

CoefficientList[Series[(1+4Sqrt[1-20x])/(5Sqrt[1-20x]), {x, 0, 20}], x]  (* Harvey P. Dale, Mar 30 2011 *)
Join[{1}, Table[5^(n - 1)*Binomial[2*n, n], {n, 1, 50}]] (* G. C. Greubel, Dec 31 2017 *)

Prog

(Magma) [(4*0^n + 5^n*Binomial(2*n, n))/5: n in [ 0..30]]; // G. C. Greubel, Dec 31 2017
(PARI) for(n=0, 30, print1((4*0^n + 5^n*binomial(2*n, n))/5, ", ")) \\ G. C. Greubel, Dec 31 2017

Crossrefs

Cf. A069723, A088218, A099044, A099045.

Sequence in context: A219869 A072976 A143414 * A020547 A208881 A297490

Adjacent sequences: A099043 A099044 A099045 * A099047 A099048 A099049

Keyword

easy,nonn

Author

Paul Barry, Sep 24 2004

Status

approved