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, 15, 648, 55440, 7875000, 1674728055, 498078806400, 197378293432320, 100519810139548800, 63970355423583984375, 49745967806568479846400, 46413542581052579412480000, 51171212156597654150866636800

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..215

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

Adjacent sequences: A092955 A092956 A092957 * A092959 A092960 A092961

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