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A092958
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.
1
1, 15, 648, 55440, 7875000, 1674728055, 498078806400, 197378293432320, 100519810139548800, 63970355423583984375, 49745967806568479846400, 46413542581052579412480000, 51171212156597654150866636800
OFFSET
1,2
LINKS
FORMULA
a(n) = n^n*Gamma((3*n+1)/2)/Gamma((n+1)/2). - Emeric Deutsch, Jan 23 2006
MAPLE
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
a:=n->mul(sum (j-k+n, j=1..n), k=1..n): seq(a(n), n=1..13); # Zerinvary Lajos, Jun 04 2007
MATHEMATICA
Array[#^#*Gamma[3 #/2 + 1/2]/Gamma[#/2 + 1/2] &, 13] (* Michael De Vlieger, Feb 19 2019 *)
PROG
(Magma) [Round(n^n*Gamma((3*n+1)/2)/Gamma((n+1)/2)): n in [1..15]]; // G. C. Greubel, Feb 20 2019
(Sage) [n^n*gamma((3*n+1)/2)/gamma((n+1)/2) for n in (1..15)] # G. C. Greubel, Feb 20 2019
(PARI) a(n) = prod(k=0, n-1, n*(n+1)/2 + k*n); \\ Michel Marcus, Feb 20 2019
CROSSREFS
Cf. A000217.
Sequence in context: A081022 A049291 A351180 * A222268 A280179 A223203
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Mar 25 2004
EXTENSIONS
More terms from Ray G. Opao, Mar 29 2004
More terms from Emeric Deutsch, Jan 23 2006
More terms from Zerinvary Lajos, Jun 04 2007
STATUS
approved