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 A092985 a(n) is the product of first n terms of an arithmetic progression with the first term 1 and common difference n. 6
 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 * Pochhammer[1/n, n], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 05 2018 *) PROG (PARI) vector(21, n, my(m=n-1); prod(j=0, m-1, j*m+1)) \\ G. C. Greubel, Mar 04 2020 (Magma) [1] cat [ (&*[j*n+1: j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Mar 04 2020 (Sage) [product(j*n+1 for j in (0..n-1)) for n in (0..20)] # G. C. Greubel, Mar 04 2020 (GAP) List([0..20], n-> Product([0..n-1], j-> j*n+1) ); # G. C. Greubel, Mar 04 2020 CROSSREFS Cf. A057237, A092987. Main diagonal of A256268. Sequence in context: A062497 A056066 A174483 * A331196 A181588 A084880 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

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Last modified November 30 12:40 EST 2022. Contains 358441 sequences. (Running on oeis4.)