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A254286 Expansion of (1-(1-256*x)^(1/4)) / (64*x). 4
1, 96, 14336, 2523136, 484442112, 98180268032, 20645907791872, 4459516083044352, 983075545417777152, 220208922173582082048, 49967406340478261526528, 11459191854083014643417088, 2651480699775516003646046208, 618173786004806016850049630208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

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)

MAPLE

a:=series((1-(1-256*x)^(1/4))/(64*x), x=0, 14): seq(coeff(a, x, n), n=0..13); # Paolo P. Lava, Mar 27 2019

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 *)

CROSSREFS

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

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

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)