|
%I #21 Aug 14 2019 16:09:03
%S 1,1,3,1,15,15,1,28,35,210,105,1,45,210,630,1575,3150,945,1,66,495,
%T 462,1485,13860,5775,13860,51975,51975,10395,1,91,1001,3003,3003,
%U 45045,42042,105105,45045,630630,525525,315315,1576575,945945,135135
%N 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.
%C The length of row n is given by A000041(n).
%C 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.
%C Has the same structure as the triangles in A036036, A096162, A115621 and A257468.
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy], pp. 831-832.
%e Brackets group all partitions of the same length when there is more than one partition.
%e n/m 1 2 3 4 5
%e 1: 1
%e 2: 1 3
%e 3: 1 15 15
%e 4: 1 [28 35] 210 105
%e 5: 1 [45 210] [630 1575] 3150 945
%e ...
%e n = 6: 1 [66 495 462] [1485 13860 5775] [13860 51975] 51975 0395
%e Replacing the bracketed numbers by their sums yields the triangle of A156289.
%t (* triangle2574868[] and triangle096162[] are defined as functions triangle[] in the respective sequences A257468 and A096162 *)
%t triangle[n_] := triangle257468[n]/triangle096162[n]
%t a[n_] := Flatten[triangle[n]]
%t a[7] (* data *)
%Y Cf. A000041, A036040, A036036, A096162, A115621, A156289, A257468.
%K nonn,tabf
%O 1,3
%A _Hartmut F. W. Hoft_, Apr 26 2015
%E Edited by _Wolfdieter Lang_, May 11 2015
|
