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Search: id:A136556
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| 1, 1, 3, 35, 1365, 169911, 67945521, 89356415775, 396861704798625, 6098989894499557055, 331001552386330913728641, 64483955378425999076128999167, 45677647585984911164223317311276545
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OFFSET
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0,3
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COMMENT
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Number of n x n binary matrices without zero rows and with distinct rows up to permutation of rows, cf. A014070.
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(2^n,k).
a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*(2^n-1)^k. G.f.: Sum_{n>=0} ln(1+2^n*x)^n/((1+2^n*x)*n!).
G.f.: A(x) = Sum_{n>=0} (1 + 2^n*x)^-1 * log(1 + 2^n*x)^n / n!.
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 35*x^3 + 1365*x^4 + 169911*x^5 +...
A(x) = (1+x)^-1 + (1+2x)^-1*log(1+2x) + (1+4x)^-1*log(1+4x)^2/2! + (1+8x)^-1*log(1+8x)^3/3! +...
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PROGRAM
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(PARI) a(n)=binomial(2^n-1, n) (PARI) /* As coefficient of x^n in the g.f.: */ {a(n)=polcoeff(sum(i=0, n, (1+2^i*x+x*O(x^n))^-1*log(1+2^i*x+x*O(x^n))^i/i!), n)}
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CROSSREFS
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Cf. A136555; A014070, A136505, A136506; A136557.
Cf. A066384.
Adjacent sequences: A136553 A136554 A136555 this_sequence A136557 A136558 A136559
Sequence in context: A062699 A012767 A136525 this_sequence A006098 A012499 A125530
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 07 2008; Paul Hanna and Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 15 2008
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EXTENSIONS
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Edited by njas, Jan 26 2008
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