|
%I #34 May 02 2022 08:14:05
%S 1,1,11,330,19140,1818300,256380300,50250538800,13065140088000,
%T 4350691649304000,1805537034461160000,913601739437346960000,
%U 553642654099032257760000,395854497680808064298400000
%N Hendecagorials: n-th polygorial for k=11.
%H G. C. Greubel, <a href="/A084944/b084944.txt">Table of n, a(n) for n = 0..220</a>
%H Daniel Dockery, <a href="https://web.archive.org/web/20140617132401/http://danieldockery.com/res/math/polygorials.pdf">Polygorials, Special "Factorials" of Polygonal Numbers</a>, preprint, 2003.
%F a(n) = polygorial(n, 11) = (A000142(n)/A000079(n))*A084949(n) = (n!/2^n)*Product_{i=0..n-1} (9*i+2) = (n!/2^n)*9^n*Pochhammer(2/9, n) = (n!/2^n)*9^n*GAMMA(n+2/9)/GAMMA(2/9).
%F D-finite with recurrence 2*a(n) = n*(9*n-7)*a(n-1). - _R. J. Mathar_, Mar 12 2019
%p a := n->n!/2^n*product(9*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k - 2), n]]; Array[polygorial[11, #] &, 16, 0] (* _Robert G. Wilson v_, Dec 13 2016 *)
%Y Cf. A006472, A001044, A000680, A084939, A084940, A084941, A084942, A084943, A085356.
%K easy,nonn
%O 0,3
%A Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003
|
