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 A273325 Number of endofunctions on [2n] such that the minimal cardinality of the nonempty preimages equals n. 2
 1, 2, 36, 300, 1960, 11340, 60984, 312312, 1544400, 7438860, 35103640, 162954792, 746347056, 3380195000, 15164074800, 67476121200, 298135873440, 1309153089420, 5717335239000, 24847720451400, 107520292479600, 463440029892840, 1990477619679120, 8521600803066000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(0) = 1 by convention. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 1+(8*x+1)*2*x/(1-4*x)^(5/2). a(n) = C(2*n,n)*C(2*n,2) for n>0, a(0)=1. a(n) = 2*C(2*(n-1),n-1)*(2*n-1)^2, a(0)=1. a(n) = 2*(2*n-1)^2*a(n-1)/((n-1)*(2*n-3)) for n>1, a(n) = 2^n for n=0..1. a(n) = A245687(2n,n). a(n) = A000108(n)*A213820(n) = 2*A000108(n)*A002414(n) for n>0, a(0)=1. Sum_{n>=0} 1/a(n) = 1 - log(sqrt(3)+2)*Pi/6 + 4*G/3, where G is Catalan's constant (A006752). - Amiram Eldar, Mar 12 2023 EXAMPLE a(1) = 2: 12, 21. a(2) = 36: 1122, 1133, 1144, 1212, 1221, 1313, 1331, 1414, 1441, 2112, 2121, 2211, 2233, 2244, 2323, 2332, 2424, 2442, 3113, 3131, 3223, 3232, 3311, 3322, 3344, 3434, 3443, 4114, 4141, 4224, 4242, 4334, 4343, 4411, 4422, 4433. MAPLE a:= proc(n) option remember; `if`(n<2, 2^n, 2*(2*n-1)^2*a(n-1)/((n-1)*(2*n-3))) end: seq(a(n), n=0..30); MATHEMATICA a[n_] := (2*n^3 + n^2 - n) * CatalanNumber[n]; a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Mar 12 2023 *) CROSSREFS Cf. A000108, A002414, A006752, A213820, A245687. Sequence in context: A074426 A082636 A242533 * A035603 A126735 A229679 Adjacent sequences: A273322 A273323 A273324 * A273326 A273327 A273328 KEYWORD nonn,easy AUTHOR Alois P. Heinz, May 20 2016 STATUS approved

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