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 A245141 Number of endofunctions f on [2n] that are self-inverse on [n]. 3
 1, 3, 50, 1626, 83736, 6026120, 571350096, 67996818960, 9862902275456, 1700092943088768, 342087177215788800, 79115601821198404352, 20779757607847901690880, 6133520505473954148381696, 2017134796016735182500521984, 733523863838078950241395968000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) counts endofunctions f:{1,...,2n}-> {1,...,2n} with f(f(i))=i for all i in {1,...,n}. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) = Sum_{i=0..n} C(n,i)^2 * i! * A000085(n-i) * (2*n)^(n-i). a(n) = A245348(2n,n). EXAMPLE a(1) = 3: (1,1), (1,2), (2,1). MAPLE g:= proc(n) g(n):= `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end: a:= n-> add(binomial(n, i)^2*i!*g(n-i)*(2*n)^(n-i), i=0..n): seq(a(n), n=0..20); CROSSREFS Cf. A000085, A245348. Column k=2 of A246070. Sequence in context: A246283 A326250 A308331 * A203239 A279970 A217767 Adjacent sequences:  A245138 A245139 A245140 * A245142 A245143 A245144 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 21 2014 STATUS approved

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Last modified September 25 22:55 EDT 2020. Contains 337346 sequences. (Running on oeis4.)