A114161 E.g.f.: (3-log(1-2*x))/(1-2*x)^(1/2).

3, 5, 17, 91, 667, 6213, 70233, 933819, 14277555, 246772485, 4757596065, 101218975515, 2355535057995, 59520844736325, 1622874515042025, 47490277029572475, 1484579154624005475, 49374909670517201925

Offset: 0

Author

Creighton Dement, Nov 14 2005

Keywords

• nonn

References

• C. Dement, Floretion Integer Sequences (work in progress)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A114160.

Programs

Mathematica

Range[0, 17]!CoefficientList[ Series[(3 - Log[1 - 2x])/Sqrt[(1 - 2x)], {x, 0, 17}], x] (* or *)
f[n_] := FullSimplify[ 2^n*Gamma[n + 1/2]/Sqrt[Pi]*(3 + PolyGamma[n + 1/2] + EulerGamma + 2Log[2])]; Table[ f[n], {n, 0, 17}] (* Robert G. Wilson v *)

PARI

{ my(x = xx + O(xx^30)); Vec(serlaplace((3-log(1-2*x))/(1-2*x)^(1/2))) } \\ Michel Marcus, Jul 06 2015

Formula

a(n) = 2^n*GAMMA(n+1/2)/Pi^(1/2)*(3+Psi(n+1/2) + gamma + 2*log(2)). - Vladeta Jovovic

Extensions

E.g.f. from Vladeta Jovovic

More terms from Robert G. Wilson v, Nov 15 2005