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A108958
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Number of unordered pairs of distinct length-n binary words having the same number of 1's.
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1
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0, 1, 6, 27, 110, 430, 1652, 6307, 24054, 91866, 351692, 1350030, 5196204, 20050108, 77542376, 300507427, 1166737574, 4537436578, 17672369756, 68922740122
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Equals row sums of triangle A143418, starting with a(2). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2008]
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FORMULA
| a(n) = sum(binomial(binomial(n, k), 2), k=0..n);
a(n) = binomial(2*n-1, n-1)-2^(n-1) = A088218(n)-A011782(n). E.g.f.: exp(2*x)*(BesselI(0, 2*x)-1)/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 24 2005
a(n)=(1/2)*sum(i+j>n,0<=i,j<=n,binomial(i+j,i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 26 2006
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EXAMPLE
| a(3) = 6 because the pairs are {001,010}, {001,100}, {010,100},
{011,101}, {011,110}, {101,110}
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MAPLE
| with(combinat) a := proc(n) sum(binomial(binomial(n, k), 2), k=0..n) end;
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CROSSREFS
| A143418 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2008]
Sequence in context: A022634 A094788 A003517 * A005284 A198694 A014825
Adjacent sequences: A108955 A108956 A108957 * A108959 A108960 A108961
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KEYWORD
| easy,nonn
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AUTHOR
| Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca), Jul 22 2005
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