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A129890
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Difference between the double factorial of the n-th nonnegative even number and the double factorial of the n-th nonnegative odd number.
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2
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1, 5, 33, 279, 2895, 35685, 509985, 8294895, 151335135, 3061162125, 68000295825, 1645756410375, 43105900812975, 1214871076343925, 36659590336994625, 1179297174137457375, 40288002704636061375, 1456700757237661060125
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OFFSET
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0,2
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COMMENTS
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In other words, a(n) = b(2n)-b(2n-1), where b = A006882. - N. J. A. Sloane, Dec 14 2011
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REFERENCES
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N. Ochiumi, On the total sum of number of nodes covering a given number of leaves in an unordered binary tree; http://www.math.tohoku.ac.jp/~sa9d05/cos2011/abst/ochiumi.pdf.
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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a(n)=(2*n)!!-(2*n-1)!!, with n>=1.
E.g.f.: 2/((1-2*x)^2)-1/[(1-2*x)*sqrt(1-2*x)] - Sergei N. Gladkovskii, Dec 04 2011
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EXAMPLE
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2!!-1!!=2-1=1
4!!-3!!=8-3=5
6!!-5!!=48-15=33
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MAPLE
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P:=proc(n) local a, i, j, k, w; for i from 1 by 1 to n do k:=product(2*j, j=1..i); w:=product(2*j-1, j=1..i); a:=k-w; print(a) od; end: P(20);
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CROSSREFS
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Cf. A006882, A122649, A202212.
Sequence in context: A135075 A215671 A049377 * A120733 A218496 A144792
Adjacent sequences: A129887 A129888 A129889 * A129891 A129892 A129893
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007
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STATUS
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approved
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