A254286 Expansion of (1 - (1-256*x)^(1/4)) / (64*x).

1, 96, 14336, 2523136, 484442112, 98180268032, 20645907791872, 4459516083044352, 983075545417777152, 220208922173582082048, 49967406340478261526528, 11459191854083014643417088, 2651480699775516003646046208, 618173786004806016850049630208

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

G.f.: (1 - (1-256*x)^(1/4)) / (64*x).

a(n) ~ 256^n / (Gamma(3/4) * n^(5/4)).

Recurrence: (n+1)*a(n) = 64*(4*n-1)*a(n-1).

a(n) = 256^n * Gamma(n+3/4) / (Gamma(3/4) * Gamma(n+2)).

E.g.f.: hypergeom([3/4], [2], 256*x). - Vaclav Kotesovec, Jan 28 2015

From Peter Bala, Sep 01 2017: (Start)

a(n) = (-1)^n*binomial(1/4, n+1)*4^(4*n+1). Cf. A000108(n) = (-1)^n*binomial(1/2, n+1)*2^(2*n+1).

a(n) = 16^n*A025749(n+1); a(n) = 32^n*A048779(n+1).

(End)

Mathematica

CoefficientList[Series[(1-(1-256*x)^(1/4)) / (64*x), {x, 0, 20}], x]
CoefficientList[Series[Hypergeometric1F1[3/4, 2, 256*x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2015 *)

Prog

(Magma) [Round(2^(8*n)*Gamma(n+3/4)/(Gamma(3/4)*Gamma(n+2))): n in [0..30]]; // G. C. Greubel, Aug 10 2022
(SageMath) [2^(8*n)*rising_factorial(3/4, n)/factorial(n+1) for n in (0..30)] # G. C. Greubel, Aug 10 2022

Crossrefs

Cf. A000108, A008545, A025749, A048779, A254282, A254287.

Sequence in context: A189909 A189903 A189159 * A216039 A208443 A183418

Adjacent sequences: A254283 A254284 A254285 * A254287 A254288 A254289

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 27 2015

Status

approved