A257490 Irregular triangle read by rows in which the n-th row lists multinomials (A036040) for partitions of 2n which have only even parts in Abramowitz-Stegun ordering.

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

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 Abramowitz-Stegun.

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. 831-832.

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: A113378 A365162 A178657 * A156289 A368493 A095922

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