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A060690
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a(n) = C(2^n + n - 1, n).
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20
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1, 2, 10, 120, 3876, 376992, 119877472, 131254487936, 509850594887712, 7145544812472168960, 364974894538906616240640, 68409601066028072105113098240, 47312269462735023248040155132636160
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OFFSET
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0,2
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COMMENTS
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Also the number of n X n (0,1) matrices modulo rows permutation (by symmetry this is the same as the number of (0,1) matrices modulo columns permutation), i.e. the number of equivalence classes where two matrices A and B are equivalent if one of them is the result of permuting the rows of the other. The total number of (0,1) matrices is in sequence A002416.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,59
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FORMULA
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a(n) = [x^n] 1/(1-x)^(2^n).
a(n) = (1/n!)*Sum((-1)^(n-k)*Stirling1(n, k)*2^(k*n), k=0..n). - Vladeta Jovovic, May 28 2004
a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(2^n+n,k) = Sum_{k=0..n} Stirling1(n,k)*(2^n+n-1)^k. G.f.: Sum_{n>=0} (-ln(1-2^n*x))^n/n!. - Paul Hanna and Vladeta Jovovic, Jan 21 2008
G.f.: A(x) = Sum_{n>=0} [ -log(1 - 2^n*x)]^n / n!. More generally, Sum_{n>=0} [ -log(1 - q^n*x)]^n/n! = Sum_{n>=0} C(q^n+n-1,n)*x^n ; also Sum_{n>=0} log(1 + q^n*x)^n/n! = Sum_{n>=0} C(q^n,n)*x^n. - Paul D. Hanna, Dec 29 2007
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MAPLE
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with(combinat): for n from 1 to 20 do printf(`%d, `, binomial(2^n+n-1, n)) od:
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MATHEMATICA
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Table[Binomial[2^n+n-1, n], {n, 0, 20}] (* From Harvey P. Dale, Apr 19 2012 *)
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PROG
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(PARI) a(n)=binomial(2^n+n-1, n)
(PARI) {a(n)=polcoeff(sum(k=0, n, (-log(1-2^k*x +x*O(x^n)))^k/k!), n)} - Paul D. Hanna, Dec 29 2007
(PARI) { for (n=0, 59, write("b060690.txt", n, " ", binomial(2^n + n - 1, n)); ) } [From Harry J. Smith, Jul 09 2009]
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CROSSREFS
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Cf. A002416, A060336, A088309, A132683, A132684.
Sequence in context: A110951 A172477 A120597 * A005617 A013038 A005321
Adjacent sequences: A060687 A060688 A060689 * A060691 A060692 A060693
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001
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EXTENSIONS
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More terms from James A. Sellers, Apr 20 2001
Edited by N. J. A. Sloane, Mar 17 2008
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STATUS
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approved
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