

A257490


Irregular triangle read by rows in which the nth row lists multinomials (A036040) for partitions of 2n which have only even parts in AbramowitzStegun ordering.


5



1, 1, 3, 1, 15, 15, 1, 28, 35, 210, 105, 1, 45, 210, 630, 1575, 3150, 945, 1, 66, 495, 462, 1485, 13860, 5775, 13860, 51975, 51975, 10395, 1, 91, 1001, 3003, 3003, 45045, 42042, 105105, 45045, 630630, 525525, 315315, 1576575, 945945, 135135
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OFFSET

1,3


COMMENTS

The length of row n is given by A000041(n).
Each entry in this irregular triangle is the quotient of the respective entries in A257468 and A096162, which is the multinomial called M_3 in AbramowitzStegun.
Has the same structure as the triangles in A036036, A096162, A115621 and A257468.


LINKS

Table of n, a(n) for n=1..44.
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], pp. 831832.


EXAMPLE

Brackets group all partitions of the same length when there is more than one partition.
n/m 1 2 3 4 5
1: 1
2: 1 3
3: 1 15 15
4: 1 [28 35] 210 105
5: 1 [45 210] [630 1575] 3150 945
...
n = 6: 1 [66 495 462] [1485 13860 5775] [13860 51975] 51975 0395
Replacing the bracketed numbers by their sums yields the triangle of A156289.


MATHEMATICA

(* triangle2574868[] and triangle096162[] are defined as functions triangle[] in the respective sequences A257468 and A096162 *)
triangle[n_] := triangle257468[n]/triangle096162[n]
a[n_] := Flatten[triangle[n]]
a[7] (* data *)


CROSSREFS

Cf. A000041, A036040, A036036, A096162, A115621, A156289, A257468.
Sequence in context: A193966 A113378 A178657 * A156289 A095922 A263632
Adjacent sequences: A257487 A257488 A257489 * A257491 A257492 A257493


KEYWORD

nonn,tabf


AUTHOR

Hartmut F. W. Hoft, Apr 26 2015


EXTENSIONS

Edited by Wolfdieter Lang, May 11 2015


STATUS

approved



