cp's OEIS Frontend

A376673 Least number whose maximum frequency in a fixed row of A036038 (or A078760) is equal to n, i.e., least number m such that A376663(m) = n, or 0 if no such number exists.

%I A376673 #10 Oct 05 2024 14:00:58
%S A376673 1,56,166320,4084080,1396755360,698377680,146659312800,1075501627200,
%T A376673 37104806138400,3710480613840000,296838449107200,86825246363856000,
%U A376673 96472495959840000,36466603472819520000,35251050023725536000,272194921062320256000,408292381593480384000
%N A376673 Least number whose maximum frequency in a fixed row of A036038 (or A078760) is equal to n, i.e., least number m such that A376663(m) = n, or 0 if no such number exists.
%C A376673 After a(36), the sequence continues (where "?" represents terms that are either 0 or greater than 10^29): ?, 3059734941813910128088320000, ?, ?, 64254433778092112689854720000. After a(41), all terms are either 0 or greater than 10^29.
%C A376673 The terms a(1), a(3), ..., a(15), a(24), a(26), ..., a(36), a(38), a(41) are all in A025487, but a(16), ..., a(23), a(25) are all divisible by 17^2 but not by 13^2.
%H A376673 Pontus von Brömssen, <a href="/A376673/b376673.txt">Table of n, a(n) for n = 1..36</a>
%e A376673 First few terms and their representations as multinomial coefficients (corresponding to partitions with sum A376664(n)):
%e A376673   a(1) =          1 = 0!;
%e A376673   a(2) =         56 = 8!/(1!*1!*6!) = 8!/(3!*5!);
%e A376673   a(3) =     166320 = 12!/(1!*1!*1!*4!*5!) = 12!/(1!*1!*2!*2!*6!) = 12!/(2!*2!*3!*5!);
%e A376673   a(4) =    4084080 = 17!/(1!*1!*1!*4!*10!) = 17!/(1!*2!*5!*9!) = 17!/(2!*2!*3!*10!) = 17!/(4!*6!*7!);
%e A376673   a(5) = 1396755360 = 19!/(1!*1!*1!*1!*1!*4!*10!) = 19!/(1!*1!*1!*2!*5!*9!) = 19!/(1!*1!*2!*2!*3!*10!) = 19!/(1!*1!*4!*6!*7!) = 19!/(3!*4!*5!*7!).
%Y A376673 First column of A376667.
%Y A376673 Cf. A025487, A036038, A078760, A376376, A376663, A376664.
%K A376673 nonn
%O A376673 1,2
%A A376673 _Pontus von Brömssen_, Oct 02 2024