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A084940 Heptagorials: n-th polygorial for k=7. 20

%I

%S 1,1,7,126,4284,235620,19085220,2137544640,316356606720,

%T 59791398670080,14050978687468800,4018579904616076800,

%U 1374354327378698265600,553864793933615401036800,259762588354865623086259200

%N Heptagorials: n-th polygorial for k=7.

%H Daniel Dockery, <a href="http://danieldockery.com/res/math/polygorials.pdf"> Polygorials, Special "Factorials" of Polygonal Numbers</a>

%F a(n) = polygorial(n, 7) = (A000142(n)/A000079(n))*A047055(n) = (n!/2^n)*Product_{i=0..n-1}(5*i+2) = (n!/2^n)*5^n*Pochhammer(2/5, n) = (n!/2^n)*5^n*GAMMA(n+2/5)*sin(2*Pi/5)*GAMMA(3/5)/Pi.

%p a := n->n!/2^n*mul(5*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[7, #] &, 16, 0] (* _Robert G. Wilson v_, Dec 26 2016 *)

%o (PARI) a(n)=n!/2^n*prod(i=1,n,5*i-3) \\ _Charles R Greathouse IV_, Dec 13 2016

%Y Cf. A006472, A001044, A000680, A084939, A084941, A084942, A084943, A084944, A085356.

%K easy,nonn,changed

%O 0,3

%A Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003

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Last modified February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)