This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182400 Integral factorial ratio sequence: a(n) = (2*n)!*(8*n)!/(n!*(4*n)!*(5*n)!). 4
 1, 28, 1716, 118864, 8684340, 653817528, 50181947376, 3903669874104, 306689672988468, 24278779897856848, 1933612147959994216, 154751222973374578656, 12435284300689518633456, 1002664938117354309314220, 81080672610600385236492840, 6573062133232532447808798864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For any nonnegative integers m, n the ratio (2*m)!*(2*n)!/(m!*(m+n)!*n!) provides an integer (theorem attributed to Catalan, see Umberto Scarpis in References), and this sequence is the case m = 4*n. REFERENCES Umberto Scarpis, Sui numeri primi e sui problemi dell'analisi indeterminata in Questioni riguardanti le matematiche elementari, Nicola Zanichelli Editore (1924-1927, third edition), page 11. LINKS Bruno Berselli, Table of n, a(n) for n = 0..100 Alexander Borisov, Quotient singularities, integer ratios of factorials and the Riemann Hypothesis, International Mathematics Research Notices, Vol. 2008, Article ID rnn052, page 2 (Theorem 2). Jonathan W. Bober, Factorial ratios, hypergeometric series, and a family of step functions, 2007, arXiv:0709.1977v1 [math.NT], page 3 (Theorem 1.2, formula 8: case a=1, b=4). FORMULA a(n) = (-1024)^n*binomial(4*n-1/2,5*n). From Ilya Gutkovskiy, Jan 31 2017: (Start) G.f.: 5F4(1/8,3/8,1/2,5/8,7/8; 1/5,2/5,3/5,4/5; 262144*x/3125). E.g.f.: 5F5(1/8,3/8,1/2,5/8,7/8; 1/5,2/5,3/5,4/5,1; 262144*x/3125). a(n) ~ 2^(18*n+1/2)/(sqrt(Pi*n)*5^(5*n+1/2)). (End) MATHEMATICA Table[((2 n)! (8 n)!)/(n! (4 n)! (5 n)!), {n, 0, 15}] PROG (MAGMA) [Factorial(2*m)*Factorial(2*n)/(Factorial(m)*Factorial(m+n)*Factorial(n)) where m is 4*n: n in [0..15]]; (Maxima) makelist((-1024)^n*binomial(4*n-1/2, 5*n), n, 0, 15); CROSSREFS Cf. A000984 (m = n), A005810 (m = 2*n), A211419 (m = 3*n). Sequence in context: A194190 A190397 A004705 * A197438 A263026 A294192 Adjacent sequences:  A182397 A182398 A182399 * A182401 A182402 A182403 KEYWORD nonn,easy AUTHOR Bruno Berselli, Apr 27 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 14 06:50 EDT 2019. Contains 327995 sequences. (Running on oeis4.)