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 A185025 Triangular array read by rows. T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} that have exactly k 2-cycles for n >= 0 and 0 <= k <= floor(n/2). 1
 1, 1, 3, 1, 18, 9, 163, 90, 3, 1950, 1100, 75, 28821, 16245, 1575, 15, 505876, 283122, 33810, 735, 10270569, 5699932, 780150, 26460, 105, 236644092, 130267440, 19615932, 884520, 8505, 6098971555, 3332614725, 538325550, 29619450, 467775, 945 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS It appears that as n gets large, row n conforms to a Poisson distribution with mean = 1/2.  In other words (as n gets large) T(n,k) approaches n^n/(2^k*k!*e^(1/2)) Note that Sum_{k=1,...floor(n/2) T(n,k)*k = A081131(n). Column for k=0 is A089466. LINKS FORMULA E.g.f.: exp(T(x)^2/2*(y-1))/(1 - T(x)) where T(x) is the e.g.f. for A000169. EXAMPLE 1, 1, 3,          1, 18,         9, 163,        90,         3, 1950,       1100,       75, 28821,      16245,      1575,      15, 505876,     283122,     33810,     735, 10270569,   5699932,    780150,    26460,    105, 236644092,  130267440,  19615932,  884520,   8505, 6098971555, 3332614725, 538325550, 29619450, 467775, 945 MATHEMATICA nn=10; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[Exp[t^2/2(y-1)]/(1-t), {x, 0, nn}], {x, y}]//Grid CROSSREFS Sequence in context: A071210 A051141 A068141 * A051238 A283150 A307064 Adjacent sequences:  A185022 A185023 A185024 * A185026 A185027 A185028 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Dec 24 2012 STATUS approved

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)