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A122400
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Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1.
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25
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1, 1, 4, 31, 338, 4769, 82467, 1687989, 39905269, 1069863695, 32071995198, 1062991989013, 38596477083550, 1523554760656205, 64961391010251904, 2975343608212835855, 145687881987604377815, 7594435556630244257213
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (1/n!)* Sum_{k=0..n} Stirling1(n,k)*A122399(k).
G.f.: Sum_{n>=0} (1+x)^(n^2) / (1 + (1+x)^n)^(n+1). - Paul D. Hanna, Mar 23 2018
a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491726382774188556341627278..., r = 0.8737024332396683304965683047207192982139922672025395099... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0, and c = 0.2796968489586733500739737080739303725411427162653658... . - Vaclav Kotesovec, May 07 2014
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MAPLE
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A122399 := proc(n) option remember ; add( combinat[stirling2](n, k)*k^n*k!, k=0..n) ; end: A122400 := proc(n) option remember ; add( combinat[stirling1](n, k)*A122399(k), k=0..n)/n! ; end: for n from 0 to 30 do printf("%d, ", A122400(n)) ; od ; # R. J. Mathar, May 18 2007
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MATHEMATICA
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CROSSREFS
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KEYWORD
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easy,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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