login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

License Agreements, Terms of Use, Privacy Policy. .

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