A020042 - OEIS

A020042

a(n) = round( Gamma(n+1/4)/Gamma(1/4) ).

1, 0, 0, 1, 2, 10, 51, 319, 2310, 19061, 176310, 1807181, 20330789, 249052162, 3299941145, 47024161317, 717118460090, 11653174976468, 201017268344078, 3668565147279424, 70619879085128903, 1430052551473860293

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OFFSET

0,5

COMMENTS

Gamma(n+1/4)/Gamma(1/4) = 1, 1/4, 5/16, 45/64, 585/256, 9945/1024, 208845/4096, 5221125/16384, 151412625/65536, ... - R. J. Mathar, Sep 04 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..450

MAPLE

Digits := 64:f := proc(n, x) round(GAMMA(n+x)/GAMMA(x)); end;

seq( round(pochhammer(1/4, n)), n=0..30); # G. C. Greubel, Dec 06 2019

MATHEMATICA

Table[Round[Pochhammer[1/4, n]], {n, 0, 30}] (* G. C. Greubel, Dec 06 2019 *)

PROG

(PARI) x=1/4; vector(30, n, round(gamma(n-1+x)/gamma(x)) ) \\ G. C. Greubel, Dec 06 2019

(Magma) [Round(Gamma(n+1/4)/Gamma(1/4)): n in [0..30]]; // G. C. Greubel, Dec 06 2019

(Sage) [round(rising_factorial(1/4, n)) for n in (0..30)] # G. C. Greubel, Dec 06 2019

CROSSREFS

Cf. A007696, A020087, A020132.

Sequence in context: A037717 A019476 A019475 * A353289 A307208 A075436

Adjacent sequences: A020039 A020040 A020041 * A020043 A020044 A020045

KEYWORD

nonn

AUTHOR

Simon Plouffe

STATUS

approved