Asymptotic estimates of Stirling numbers and related asymptotic problems 1993
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Author: by Nico M. Temme
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Abstract: F12.38> S(4; 1) = 1, S(4; 2) = 7, S(4; 3) = 6, S(4; 4) = 1. There is the handy recursion S(n; m) = mS(n \Gamma 1; m) + S(n \Gamma 1; m \Gamma 1) to compute them. The (signless) Stirling numbers of the first kind js(n; k)j enumerate the number of permutations of the set f1; : : : ; ng with exactly m cycles. Example. (1)(2)(3) (12)(3); (13)(2); (23)(1) (123); (132); whence js(3; 1)j = 2, js(3; 2)j = 3, js(3;<
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