A136101 -id:A136101 - cp's OEIS frontend

A138533 Resort the multinomial sequence A036038 by source partition as described in A126442, A129306 and A136101.

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

Offset: 1

Alford Arnold, Mar 27 2008

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.

			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
...

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

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

A140691 Suppress the zeros in A126441 and resort the natural numbers as illustrated in sequence A136101.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 6, 16, 17, 19, 23, 31, 10, 13, 32, 33, 35, 39, 47, 63, 18, 21, 27, 12, 14, 64, 65, 67, 71, 79, 95, 127, 34, 37, 43, 55, 20, 25, 22, 29, 128, 129, 131, 135, 143, 159, 191, 255, 66, 69, 75, 87, 111, 36, 41, 51, 38, 45, 59, 24, 26, 30, 256, 257, 259

Offset: 1

Alford Arnold, May 23 2008

nonn

Table A138138 (a shell model) is another sequence illustrating row patterns for numeric partitions.

			A136101(11) is 36 and is 2*2*3*3 corresponding to the partition 2+2 which maps to 6 in A136101 so A140691(11) is 6.

Cf. A025487 A138138.

cp's OEIS Frontend

A138533 Resort the multinomial sequence A036038 by source partition as described in A126442, A129306 and A136101.

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