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%I #28 Sep 08 2022 08:45:13
%S 1,15,648,55440,7875000,1674728055,498078806400,197378293432320,
%T 100519810139548800,63970355423583984375,49745967806568479846400,
%U 46413542581052579412480000,51171212156597654150866636800
%N a(1) = 1, a(2) = (1+2)*(2+3), a(3) = (1+2+3)*(2+3+4)*(3+4+5), ... etc. Or a(n) = (T(n))*(T(n)+n)*(T(n)+2n)*(T(n)+3n)*... n terms. where T(n) = n(n+1)/2 given by A000217.
%H Michael De Vlieger, <a href="/A092958/b092958.txt">Table of n, a(n) for n = 1..215</a>
%F a(n) = n^n*Gamma((3*n+1)/2)/Gamma((n+1)/2). - _Emeric Deutsch_, Jan 23 2006
%p a:=n->n^n*GAMMA(3*n/2+1/2)/GAMMA(n/2+1/2): seq(a(n),n=1..18); # _Emeric Deutsch_, Jan 23 2006
%p a:=n->mul(sum (j-k+n,j=1..n),k=1..n): seq(a(n),n=1..13); # _Zerinvary Lajos_, Jun 04 2007
%t Array[#^#*Gamma[3 #/2 + 1/2]/Gamma[#/2 + 1/2] &, 13] (* _Michael De Vlieger_, Feb 19 2019 *)
%o (Magma) [Round(n^n*Gamma((3*n+1)/2)/Gamma((n+1)/2)): n in [1..15]]; // _G. C. Greubel_, Feb 20 2019
%o (Sage) [n^n*gamma((3*n+1)/2)/gamma((n+1)/2) for n in (1..15)] # _G. C. Greubel_, Feb 20 2019
%o (PARI) a(n) = prod(k=0, n-1, n*(n+1)/2 + k*n); \\ _Michel Marcus_, Feb 20 2019
%Y Cf. A000217.
%K easy,nonn
%O 1,2
%A _Amarnath Murthy_, Mar 25 2004
%E More terms from _Ray G. Opao_, Mar 29 2004
%E More terms from _Emeric Deutsch_, Jan 23 2006
%E More terms from _Zerinvary Lajos_, Jun 04 2007
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