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 A288312 Number of endofunctions on [2n] such that the image size equals n. 3
 1, 2, 84, 10800, 2857680, 1285956000, 880599202560, 853262368358400, 1111400775560275200, 1873276460474747328000, 3967400888465895264384000, 10313998054713896966296473600, 32291970618091110826769565696000, 119851615755915509174015455948800000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..195 FORMULA a(n) = Stirling2(2*n,n) * n! * binomial(2*n,n). a(n) = A090657(2n,n) = A101817(2n,n). a(n) ~ n^(2*n - 1/2) * 2^(4*n) / (sqrt(Pi*(1-c)) * c^n * (2-c)^n * exp(2*n)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Jun 10 2017 EXAMPLE a(1) = 2: (1,1), (2,2). MAPLE b:= proc(n, k) option remember; `if`(k=n, n!,       `if`(k=0, 0, n*(b(n-1, k-1)+b(n-1, k)*k/(n-k))))     end: a:= n-> b(2*n, n): seq(a(n), n=0..15); MATHEMATICA Table[StirlingS2[2*n, n]*(2*n)!/n!, {n, 0, 20}] (* Vaclav Kotesovec, Jun 10 2017 *) PROG (PARI) a(n)=stirling(2*n, n, 2)*n!*binomial(2*n, n); \\ Indranil Ghosh, Jul 04 2017 (Python) from mpmath import * mp.dps=100 def a(n): return int(stirling2(2*n, n)*fac(n)*binomial(2*n, n)) print [a(n) for n in range(21)] # Indranil Ghosh, Jul 04 2017 CROSSREFS Cf. A000142, A048993, A090657, A101817. Sequence in context: A215263 A265591 A157063 * A289198 A318128 A181119 Adjacent sequences:  A288309 A288310 A288311 * A288313 A288314 A288315 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 07 2017 STATUS approved

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Last modified February 25 22:55 EST 2020. Contains 332270 sequences. (Running on oeis4.)