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A138533 Resort the multinomial sequence A036038 by source partition as described in A126442, A129306 and A136101. 1
1, 2, 1, 6, 3, 1, 24, 12, 4, 1, 6, 120, 60, 20, 5, 1, 30, 10, 720, 360, 120, 30, 6, 1, 180, 60, 15, 20, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multinomials count permutations of multisets and also paths in lattices; for example, there are six paths (from null to full) through the lattice of divisors for signature 36: 2233 2323 2332 3223 3232 and 3322.

LINKS

Table of n, a(n) for n=1..29.

EXAMPLE

a(11) is six because the eleventh least prime signature in source format is 36 the signature for partition 2+2 the ninth partition and A036038(9) = 6.

The tables begin:

1.......2.......6.......24......120.....720....5040.....40320......362880

........1.......3.......12.......60.....360....2520.....20160......181440

................1.......4........20.....120.....840......6720.......60480

........................1........5.......30.....210......1680.......15120

.. ..............................1........6......42......336........3024

..........................................1.......7.......56.........504

..................................................1........8..........72

...........................................................1...........9

.......................................................................1

........................6........30.....180....1260....10080........90720

.................................10......60.....420.....3360........30240

...

CROSSREFS

Cf. A000142 A001710 A005651 (column sums) A025487 A053445.

Cf. A173333. [From Reinhard Zumkeller, Feb 19 2010]

Sequence in context: A270967 A103209 A089900 * A173333 A221915 A249619

Adjacent sequences:  A138530 A138531 A138532 * A138534 A138535 A138536

KEYWORD

nonn,tabf

AUTHOR

Alford Arnold, Mar 27 2008

STATUS

approved

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Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)