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A096131 Sum of the terms of the n-th row of triangle pertaining to A096130. 7
1, 7, 105, 2386, 71890, 2695652, 120907185, 6312179764, 375971507406, 25160695768715, 1869031937691061, 152603843369288819, 13584174777196666630, 1309317592648179024666, 135850890740575408906465 (list; graph; refs; listen; history; text; internal format)
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

Cf. A014062, A096130, A034841, A007318, A226391, A167009, A167008, A167010, A072034, A086331.

Sequence in context: A132867 A145666 A238464 * A049210 A167814 A209545

Adjacent sequences:  A096128 A096129 A096130 * A096132 A096133 A096134

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

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)