A182449 - OEIS

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A182449

The number of n-permutations whose connected components have the same size.

1, 2, 4, 15, 72, 472, 3448, 29264, 273371, 2834368, 31998904, 392958758, 5201061456, 73955306224, 1123596636018, 18177574748625, 311951144828864, 5661773589217182, 108355864447215064, 2181104926663522206, 46066653269313449442, 1018706122380363766288

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OFFSET

1,2

COMMENTS

See A003319 for definition of connected component.

a(p) = A003319(p)+1 for all prime numbers, p.

LINKS

Table of n, a(n) for n=1..22.

FORMULA

O.g.f.: Sum_{n>0} 1/(1-A003319(n)*x^n).

EXAMPLE

a(4) = 15 because there are 13 connected permutations of {1,2,3,4} (these are counted by A003319) and 21/43 and 1/2/3/4.

MATHEMATICA

nn = 20; p = Sum[n! x^n, {n, 0, nn}]; i = 1 - 1/p; a = CoefficientList[Series[i, {x, 0, nn}], x]; s = Sum[1/(1 - a[[n + 1]] x^n), {n, 1, nn}]; Drop[ CoefficientList[Series[s, {x, 0, nn}], x], 1]

CROSSREFS

Sequence in context: A020110 A290024 A292757 * A140836 A020134 A307085

Adjacent sequences: A182446 A182447 A182448 * A182450 A182451 A182452

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Apr 29 2012

STATUS

approved