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Search: id:A010551
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| A010551 |
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Multiply successively by 1,1,2,2,3,3,4,4,... |
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+0
4
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| 1, 1, 1, 2, 4, 12, 36, 144, 576, 2880, 14400, 86400, 518400, 3628800, 25401600, 203212800, 1625702400, 14631321600, 131681894400, 1316818944000, 13168189440000, 144850083840000, 1593350922240000
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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a(n) = [n/2]! * [(n+1)/2 ]! is the number of permutations p of {1, 2, 3, ..., n} such that for every i, i and p(i) have the same parity, i.e. p(i) - i is even - Avi Peretz (njk(AT)netvision.net.il), Feb 22 2001
a(n)=n!/binomial(n, floor(n/2)) - Paul Barry (pbarry(AT)wit.ie), Sep 12 2004
G.f.: Sum_{n>=0} x^n/a(n) = besseli(0, 2*x) + x*besseli(1, 2*x). - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2005
E.g.f.: 1/(1-x/2) + (1/2)/(1-x/2)*acos(1-x^2/2)/sqrt(1-x^2/4). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 28 2005
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MAPLE
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A010551 := proc(n) option remember; if n <= 1 then 1 else A010551(n-1)*trunc( (n+1)/2 ); fi; end;
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PROGRAM
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(PARI) {a(n)=local(X=x+x*O(x^n)); 1/polcoeff(besseli(0, 2*X)+X*besseli(1, 2*X), n, x)} (Hanna)
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CROSSREFS
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Cf. A064044.
Adjacent sequences: A010548 A010549 A010550 this_sequence A010552 A010553 A010554
Sequence in context: A086647 A062161 A046993 this_sequence A111942 A003701 A114500
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KEYWORD
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nonn
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AUTHOR
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markd(AT)psy.uwa.edu.au (Mark Diamond)
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