

A061163


a(n) = (10n)!*n!/((5n)!*(4n)!*(2n)!).


7



1, 630, 1385670, 3528923580, 9540949030470, 26651569523959380, 75998432812419471900, 219813190240007470094520, 642409325786050322446410310, 1892390644737640220059489996260
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OFFSET

0,2


COMMENTS

According to page 781 of the cited reference the generating function F(x) for a(n) is algebraic but not obviously so and the minimal polynomial satisfied by F(x) is quite large.
This sequence is the particular case a = 5, b = 1 of the following result (see Bober, Theorem 1.2): let a, b be nonnegative integers with a > b and GCD(a,b) = 1. Then (2*a*n)!*(b*n)!/((a*n)!*(2*b*n)!*((ab)*n)!) is an integer for all integer n >= 0. Other cases include A061162 (a = 3, b = 1), A211419 (a = 3, b = 2) and A211420(a = 4, b = 1) and A211421 (a = 4, b = 3). The o.g.f. sum {n >= 1} a(n)*z^n is algebraic over the field of rational functions Q(z) (see RodriguezVillegas).  Peter Bala, Apr 10 2012


REFERENCES

M. Kontsevich and D. Zagier, Periods, in Mathematics Unlimited  2001 and Beyond, Springer, Berlin, 2001, pp. 771808.


LINKS

Table of n, a(n) for n=0..9.
J. W. Bober, Factorial ratios, hypergeometric series, and a family of step functions, 2007, arXiv:0709.1977v1 [math.NT], Jour. of the London Math. Soc., Vol. 79, Issue 2, 422444.
F. RodriguezVillegas, Integral ratios of factorials and algebraic hypergeometric functions. arXiv:math.NT/0701362


FORMULA

n*(4*n3)*(2*n1)*(4*n1)*a(n) 10*(10*n9)*(10*n7)*(10*n3)*(10*n1)*a(n1)=0.  R. J. Mathar, Oct 26 2014


MAPLE

A061123 := n>(10*n)!*n!/((5*n)!*(4*n)!*(2*n)!);


CROSSREFS

Cf. A061163, A061164. A211419, A211420, A211421.
Sequence in context: A185849 A058832 A225390 * A045168 A270802 A119504
Adjacent sequences: A061160 A061161 A061162 * A061164 A061165 A061166


KEYWORD

easy,nonn


AUTHOR

Richard Stanley, Apr 17 2001


STATUS

approved



