OFFSET
1,2
COMMENTS
The product of the terms of the n-th row is given by A034841.
Collection of partial binary matrices: 1 to n rows of length n and a total of n entries set to one in each partial matrix. - Olivier Gérard, Aug 08 2016
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..338
FORMULA
a(n) = Sum_{k=1..n} binomial(k*n, n). - Reinhard Zumkeller, Jan 09 2005
a(n) = (1/n!) * Sum_{j=1..n} Product_{i=n*(j-1)+1..n*j} i. - Reinhard Zumkeller, Jan 09 2005 [corrected by Seiichi Manyama, Aug 17 2018]
a(n) ~ exp(1)/(exp(1)-1) * binomial(n^2,n). - Vaclav Kotesovec, Jun 06 2013
EXAMPLE
From Seiichi Manyama, Aug 18 2018: (Start)
a(1) = (1/1!) * (1) = 1.
a(2) = (1/2!) * (1*2 + 3*4) = 7.
a(3) = (1/3!) * (1*2*3 + 4*5*6 + 7*8*9) = 105.
a(4) = (1/4!) * (1*2*3*4 + 5*6*7*8 + 9*10*11*12 + 13*14*15*16) = 2386. (End)
MAPLE
A096130 := proc(n, k) binomial(k*n, n) ; end: A096131 := proc(n) local k; add( A096130(n, k), k=1..n) ; end: for n from 1 to 18 do printf("%d, ", A096131(n)) ; od ; # R. J. Mathar, Apr 30 2007
seq(add((binomial(n*k, n)), k=0..n), n=1..15); # Zerinvary Lajos, Sep 16 2007
MATHEMATICA
Table[Sum[Binomial[k*n, n], {k, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jun 06 2013 *)
PROG
(GAP) List(List([1..20], n->List([1..n], k->Binomial(k*n, n))), Sum); # Muniru A Asiru, Aug 12 2018
(PARI) a(n) = sum(k=1, n, binomial(k*n, n)); \\ Michel Marcus, Aug 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 04 2004
EXTENSIONS
More terms from R. J. Mathar, Apr 30 2007
Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of R. J. Mathar
STATUS
approved