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Search: id:A055601
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| A055601 |
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Number of n X n binary matrices with no zero rows. |
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+0
7
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| 1, 1, 9, 343, 50625, 28629151, 62523502209, 532875860165503, 17878103347812890625, 2375680873491867011912191, 1255325460068093790930770843649
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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More generally, Sum_{n>=0} m^n * q^(n^2) * exp(b*q^n*x) * x^n / n! = Sum_{n>=0} (m*q^n + b)^n * x^n / n! for all q, m, b. - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2008
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FORMULA
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a(n) = (2^n - 1 )^n. - Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
a(n)=Sum_{k=0..n} (-1)^k*C(n, k)*2^((n-k)*n).
E.g.f.: A(x) = Sum_{n>=0} 2^(n^2) * exp(-2^n*x) * x^n/n!. - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2008
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EXAMPLE
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A(x) = 1 + x + 3^2*x^2/2! + 7^3*x^3/3! + 15^4*x^4/4! +... + (2^n-1)^n*x^n/n! +... A(x) = exp(-x) + 2*exp(-2x) + 2^4*exp(-4x)*x^2/2! + 2^9*exp(-8x)*x^3/3! +...+ 2^(n^2)*exp(-2^n*x)*x^n/n! +...
This is a special case of the more general statement: Sum_{n>=0} m^n * F(q^n*x)^b * log( F(q^n*x) )^n / n! = Sum_{n>=0} x^n * [y^n] F(y)^(m*q^n + b) where F(x) = exp(x), q=2, m=1, b=-1.
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PROGRAM
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(PARI) a(n)=n!*polcoeff(sum(k=0, n, 2^(k^2)*exp(-2^k*x)*x^k/k!), n) - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2008
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CROSSREFS
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Cf. A048291.
a(n) = A092477(n,n) for n>0.
Cf. A136516.
Sequence in context: A098650 A098652 A110695 this_sequence A012812 A119756 A063068
Adjacent sequences: A055598 A055599 A055600 this_sequence A055602 A055603 A055604
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 01 2000
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