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A122400 Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1. 25
1, 1, 4, 31, 338, 4769, 82467, 1687989, 39905269, 1069863695, 32071995198, 1062991989013, 38596477083550, 1523554760656205, 64961391010251904, 2975343608212835855, 145687881987604377815, 7594435556630244257213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..375

FORMULA

a(n) = (1/n!)* Sum_{k=0..n} Stirling1(n,k)*A122399(k).

G.f.: Sum_{n>=0} ((1+x)^n - 1)^n. - Vladeta Jovovic, Sep 03 2006

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

MAPLE

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

MATHEMATICA

max = 17; CoefficientList[ Series[ 1 + Sum[ ((1 + x)^n - 1)^n, {n, 1, max}], {x, 0, max}], x] (* Jean-Fran├žois Alcover, Mar 26 2013, after Vladeta Jovovic *)

CROSSREFS

Cf. A104602, A220353, A301581, A301582, A301583, A301584.

Sequence in context: A243312 A076280 A141005 * A107725 A145160 A129271

Adjacent sequences:  A122397 A122398 A122399 * A122401 A122402 A122403

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 31 2006

EXTENSIONS

More terms from R. J. Mathar, May 18 2007

STATUS

approved

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Last modified January 22 03:32 EST 2021. Contains 340360 sequences. (Running on oeis4.)