The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A364182 a(n) = (12*n)!*(n/2)!/((6*n)!*(4*n)!*(5*n/2)!). 0
 1, 7392, 267711444, 11489451294720, 527048385075849780, 25051434899696246587392, 1217325447549161369383451760, 60050961586064738516089033457664, 2994861478939539397101967737771147060, 150602318360773064327512837557840362078208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A295477, defined by A295477(n) = (24*n)!*n! / ((12*n)!*(8*n)!*(5*n)!), is one of the 52 sporadic integral factorial ratio sequences of height 1 found by V. I. Vasyunin (see Bober, Table 2, Entry 47). Here we are essentially considering the sequence {A295477(n/2) : n >= 0}. Fractional factorials are defined in terms of the gamma function; for example, (5*n/2)! := Gamma(1 + 5*n/2). This sequence is only conjecturally an integer sequence. Conjecture: the supercongruences a(n*p^r) == a(n*p^(r-1)) (mod p^(3*r)) hold for all primes p >= 5 and all positive integers n and r. LINKS Table of n, a(n) for n=0..9. J. W. Bober, Factorial ratios, hypergeometric series, and a family of step functions, arXiv:0709.1977 [math.NT], 2007; J. London Math. Soc., 79, Issue 2, (2009), 422-444. FORMULA a(n) ~ c^n * 1/sqrt(20*Pi*n), where c = (2^12)*(3^6)/(5^3) * sqrt(5). a(n) = 82944*(12*n - 1)*(12*n - 5)(12*n - 7)*(12*n - 11)*(12*n - 13)*(12*n - 17)*(12*n - 19)*(12*n - 23)/(5*n*(n - 1)*(2*n - 1)*(2*n - 3)*(5*n - 2)*(5*n - 4)*(5*n - 6)*(5*n - 8))*a(n-2) with a(0) = 1 and a(1) = 7392 MAPLE seq( simplify((12*n)!*(n/2)!/((6*n)!*(4*n)!*(5*n/2)!)), n = 0..15); CROSSREFS Cf. A276100, A276101, A276102, A295431, A295477, A347854, A347855, A347856, A347857, A347858, A364173 - A364185. Sequence in context: A028540 A347164 A206202 * A034279 A031584 A237311 Adjacent sequences: A364179 A364180 A364181 * A364183 A364184 A364185 KEYWORD nonn,easy AUTHOR Peter Bala, Jul 13 2023 STATUS approved

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

Last modified December 4 16:44 EST 2023. Contains 367563 sequences. (Running on oeis4.)