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A096131
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Sum of the terms of the n-th row of triangle pertaining to A096130.
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11
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1, 7, 105, 2386, 71890, 2695652, 120907185, 6312179764, 375971507406, 25160695768715, 1869031937691061, 152603843369288819, 13584174777196666630, 1309317592648179024666, 135850890740575408906465
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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)
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MAPLE
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seq(add((binomial(n*k, n)), k=0..n), n=1..15); # Zerinvary Lajos, Sep 16 2007
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MATHEMATICA
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Table[Sum[Binomial[k*n, n], {k, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jun 06 2013 *)
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PROG
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(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
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CROSSREFS
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Cf. A014062, A096130, A034841, A007318, A226391, A167009, A167008, A167010, A072034, A086331, A349470.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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