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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. 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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified December 3 15:15 EST 2021. Contains 349463 sequences. (Running on oeis4.)