cp's OEIS Frontend

A376370 Square array read by antidiagonals: row n lists numbers that occur exactly n times in A036038 (or A050382 or A078760 or A318762), i.e., numbers m such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) is equal to m for exactly n integer partitions (x_1, ..., x_k).

%I A376370 #18 Oct 01 2024 12:04:44
%S A376370 2,3,10,4,12,6,5,15,20,420,7,21,30,630,120,8,24,56,840,1680,210,9,28,
%T A376370 60,1980,60060,1260,4324320,11,35,90,3003,83160,2520,21621600,7207200,
%U A376370 13,36,105,7140,180180,5040,24504480,151351200,720720
%N A376370 Square array read by antidiagonals: row n lists numbers that occur exactly n times in A036038 (or A050382 or A078760 or A318762), i.e., numbers m such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) is equal to m for exactly n integer partitions (x_1, ..., x_k).
%C A376370 Row n lists numbers m such that A376369(m) = n.
%C A376370 In case there are only finitely many solutions for a certain value of n, the rest of that row is filled with 0's.
%C A376370 Any integer k >= 2 appears exactly once in the array.
%H A376370 Pontus von Brömssen, <a href="/A376370/b376370.txt">Table of n, a(n) for n = 1..1081</a> (antidiagonals 1..46)
%e A376370 Array begins:
%e A376370   n\k|       1         2         3         4         5          6          7          8
%e A376370   ---+---------------------------------------------------------------------------------
%e A376370   1  |       2         3         4         5         7          8          9         11
%e A376370   2  |      10        12        15        21        24         28         35         36
%e A376370   3  |       6        20        30        56        60         90        105        252
%e A376370   4  |     420       630       840      1980      3003       7140       7560       9240
%e A376370   5  |     120      1680     60060     83160    180180     240240     831600     900900
%e A376370   6  |     210      1260      2520      5040     27720     166320    1441440    4084080
%e A376370   7  | 4324320  21621600  24504480  43243200  75675600  116396280  367567200  908107200
%e A376370   8  | 7207200 151351200 302702400 411863760 823727520 1816214400 2327925600 4655851200
%Y A376370 Cf. A036038, A050382, A078760, A318762, A325472 (complement of first row), A325593 (complement of the union of the first 2 rows), A376369, A376376 (first column).
%Y A376370 First five rows are A376371, A376372, A376373, A376374, A376375.
%K A376370 nonn,tabl
%O A376370 1,1
%A A376370 _Pontus von Brömssen_, Sep 22 2024