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A092271 First in a series of triangular arrays counting permutations of partitions. 4
1, 1, 1, 2, 3, 1, 6, 8, 6, 1, 24, 30, 20, 10, 1, 120, 144, 90, 40, 15, 1, 720, 840, 504, 210, 70, 21, 1, 5040, 5760, 3360, 1344, 420, 112, 28, 1, 40320, 45360, 25920, 10080, 3024, 756, 168, 36, 1, 362880, 403200, 226800, 86400, 25200, 6048, 1260, 240, 45, 1, 3628800, 3991680, 2217600, 831600, 237600, 55440, 11088, 1980, 330, 55, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Generate signatures in accordance with A086141. Map to partitions in accordance with A025487. Calculate the number of permutations in accordance with Abramowitz and Stegun, p. 831 (reference M2). Display the results as illustrated by A090774. The second array is:

    3

   20  15

   90 120  45

  504 630 420 105

  ...

Apart from the main diagonal, appears to be the same as A211603 (see also A238363) and is related to the infinitesimal generator of A008290; if so, the off-diagonal triangle entries are given by binomial(n,k)*(n-k-1)! for n >= 2 and 0 <= k <= n-2. - Peter Bala, Feb 13 2017

REFERENCES

Abramowitz and Stegun, p. 831.

LINKS

Table of n, a(n) for n=1..66.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

EXAMPLE

The array begins:

   1

   1  1

   2  3  1

   6  8  6  1

  24 30 20 10 1

  ...

MATHEMATICA

f[list_] :=Total[list]!/Apply[Times, list]/Apply[Times, Map[Length, Split[list]]!]; Table[Append[Map[f, Select[Partitions[n], Count[#, Except[1]] == 1 &]], 1], {n, 1, 10}] // Grid (* Geoffrey Critzer, Nov 07 2015 *)

CROSSREFS

Cf. A007290, A025487, A086141, A090774, A008290, A111492, A211603, A238363.

Sequence in context: A036039 A324254 A279038 * A054115 A100822 A198427

Adjacent sequences:  A092268 A092269 A092270 * A092272 A092273 A092274

KEYWORD

nonn,tabl

AUTHOR

Alford Arnold, Feb 14 2004

EXTENSIONS

More terms from Geoffrey Critzer, Nov 10 2015

STATUS

approved

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Last modified May 30 09:15 EDT 2020. Contains 334712 sequences. (Running on oeis4.)