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 A129890 Difference between the double factorial of the n-th nonnegative even number and the double factorial of the n-th nonnegative odd number. 2
 1, 5, 33, 279, 2895, 35685, 509985, 8294895, 151335135, 3061162125, 68000295825, 1645756410375, 43105900812975, 1214871076343925, 36659590336994625, 1179297174137457375, 40288002704636061375, 1456700757237661060125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In other words, a(n) = b(2n)-b(2n-1), where b = A006882. - N. J. A. Sloane, Dec 14 2011 REFERENCES 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. LINKS FORMULA 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 EXAMPLE 2!!-1!!=2-1=1 4!!-3!!=8-3=5 6!!-5!!=48-15=33 MAPLE 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); CROSSREFS Cf. A006882, A122649, A202212. Sequence in context: A135075 A215671 A049377 * A120733 A218496 A144792 Adjacent sequences:  A129887 A129888 A129889 * A129891 A129892 A129893 KEYWORD easy,nonn AUTHOR Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007 STATUS approved

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