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).
(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
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 27 2015
STATUS
approved