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A208248 Sum of the maximum cycle length over all functions f:{1,2,...,n} -> {1,2,...,n} (endofunctions). 3
0, 1, 5, 40, 431, 5826, 94657, 1795900, 38963535, 951398890, 25819760021, 770959012704, 25117397416795, 886626537549130, 33708625339151505, 1373237757290215156, 59677939242566840303, 2755753623830236494930, 134746033233724391374765, 6954962673986411576581000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is also the sum of the number of endofunctions with at least one cycle >= i for all i>=1. In other words A000312 + A101334 + A208240 + ... .

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..386

FORMULA

E.g.f.: Sum_{k>=0} 1/(1-T(x)) - exp(Sum_{i=1...k} T(x)^i/i) = A(T(x)) where A(x) is the e.g.f. for A028418 and T(x) is the e.g.f. for A000169.

MAPLE

b:= proc(n, m) option remember; `if`(n=0, m, add((j-1)!*

      b(n-j, max(m, j))*binomial(n-1, j-1), j=1..n))

    end:

a:= n-> add(b(j, 0)*n^(n-j)*binomial(n-1, j-1), j=0..n):

seq(a(n), n=0..20);  # Alois P. Heinz, May 20 2016

MATHEMATICA

nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Apply[Plus, Table[Range[0, nn]! CoefficientList[Series[1/(1-t) - Exp[Sum[t^i/i, {i, 1, n}]], {x, 0, nn}], x], {n, 0, nn-1}]]

CROSSREFS

Cf. A000169, A028418, A000312, A101334, A208231, A208240, A290932.

Sequence in context: A306029 A243671 A083304 * A290932 A258172 A304866

Adjacent sequences:  A208245 A208246 A208247 * A208249 A208250 A208251

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jan 12 2013

STATUS

approved

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Last modified November 18 17:45 EST 2019. Contains 329287 sequences. (Running on oeis4.)