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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.)