This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A092985 a(n) = Arithofactorial(n) = AF(n) is the product of first n terms of an arithmetic progression with the first term 1 and common difference n. 3
 1, 1, 3, 28, 585, 22176, 1339975, 118514880, 14454403425, 2326680294400, 478015854767451, 122087424094272000, 37947924636264267625, 14105590169042424729600, 6178966019176767549393375, 3150334059785191453342744576, 1849556085478041490537172810625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS We have the triangle 1 1 3 1 4 7 1 5 9 13 1 6 11 16 21 1 7 13 19 25 31 ... Sequence contains the product of the terms of the rows. a(n) = b(n-1) where b(n) = n^n*Gamma(n+1/n)/Gamma(1/n) and b(0) is limit n->0+ of b(n). - Gerald McGarvey, Nov 10 2007 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) = 1*(1+n)*(1+2n)*...*(n^2-n+1). a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*n^(n-k). - Vladeta Jovovic, Jan 28 2005 a(n) = n! * [x^n] 1/(1 - n*x)^(1/n) for n > 0. - Ilya Gutkovskiy, Oct 05 2018 a(n) ~ sqrt(2*Pi) * n^(2*n - 3/2) / exp(n). - Vaclav Kotesovec, Oct 05 2018 EXAMPLE a(5) = 1*6*11*16*21 = 22176. MAPLE a:= n-> mul(n*j+1, j=0..n-1): seq(a(n), n=0..20);  # Alois P. Heinz, Nov 24 2015 MATHEMATICA Flatten[{1, Table[n^(n - 1)*Pochhammer[1 + 1/n, n - 1], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 05 2018 *) CROSSREFS Cf. A057237, A092987. Main diagonal of A256268. Sequence in context: A062497 A056066 A174483 * A181588 A084880 A110259 Adjacent sequences:  A092982 A092983 A092984 * A092986 A092987 A092988 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Mar 28 2004 EXTENSIONS More terms from Erich Friedman, Aug 08 2005 Offset corrected by Alois P. Heinz, Nov 24 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)