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%I
%S 1,1,5,60,1320,46200,2356200,164934000,15173928000,1775349576000,
%T 257425688520000,45306921179520000,9514453447699200000,
%U 2350070001581702400000,674470090453948588800000,222575129849803034304000000
%N Pentagorials: n-th polygorial for k=5.
%F A084939(n) = Polygorial(n, 5) = A000142(n)/A000079(n)*A008544(n) = n!/2^n*product(3*i+2, i=0..n-1) = n!/2^n*3^n*pochhammer(2/3, n) = n!/2^n*3^n*GAMMA(n+2/3)/GAMMA(2/3)
%p a := n->n!/2^n*mul(3*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t Table[k! Pochhammer[2/3, k] (3/2)^k, {k, 0, 20}] (* _Jan Mangaldan_, Mar 20 2013 *)
%Y Cf. A006472, A001044, A000680, A084940, A084941, A084942, A084943, A084944, A085356.
%K easy,nonn
%O 0,3
%A Daniel Dockery (peritus(AT)gmail.com) Jun 13 2003
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