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A224246 The number of n-permutations that have a unique smallest cycle and this cycle contains the element 1. 1
1, 1, 3, 8, 41, 194, 1309, 9022, 79057, 689588, 7462601, 80632826, 1021071193, 13120783948, 192752054377, 2848878770774, 47617784530529, 800500650553472, 14910497765819137, 281133366288649138, 5803224036600349801, 120681837753825004796, 2734647516979262677673, 62424209302423879016558, 1535507329367939907583057 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..450

FORMULA

E.g.f.: Sum_{k>=1} Integral_((x^(k-1)/(k-1))*exp(-Sum_{i=1..k} x^i/i)/(1-x) dx).

EXAMPLE

a(4) = 8 because we have the permutations of {1,2,3,4} in cycle notation:

{{1}, {3,4,2}}, {{1}, {4,3,2}}, {{2,3,4,1}}, {{2,4,3,1}}, {{3,4,2,1}}, {{3,2,4,1}}, {{4,3,2,1}}, {{4,2,3,1}}.

MAPLE

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

      binomial(n-1, i-1)*b(n-i, `if`(t=1, i+1, t)), i=t..n))

    end:

a:= n-> b(n, 1):

seq(a(n), n=1..30);  # Alois P. Heinz, Sep 07 2020

MATHEMATICA

nn=20; Drop[Range[0, nn]! CoefficientList[Series[Sum[Integrate[x^(k-1) Exp[-Sum[x^i/i, {i, 1, k}]]/(1-x), x], {k, 1, nn}], {x, 0, nn}], x], 1]

CROSSREFS

Cf. A224245, A224244, A224219.

Sequence in context: A152394 A168468 A330527 * A128322 A337758 A038048

Adjacent sequences:  A224243 A224244 A224245 * A224247 A224248 A224249

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Apr 01 2013

STATUS

approved

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Last modified January 27 21:15 EST 2022. Contains 350653 sequences. (Running on oeis4.)