50400

Appears in sequences

• Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.at n=26A002182
• Where records occur in A038548.at n=23A004778
• cos(cos(x)-sech(x))=1-560/8!*x^8+50400/10!*x^10-4403520/12!*x^12...at n=5A013487
• Numbers k such that sigma(k) >= 4*k.at n=3A023198
• Theta series of A*_8 lattice.at n=61A023920
• a(n) = (3*n+1)! / (24*n).at n=2A028917
• Triangular table of 2^n *(n+k)! / ((n-k)! * k! * 4^k).at n=31A043302
• a(n) = n*(n-1)^2*(n-2).at n=14A047928
• Smallest positive number of "triangular" shuffles of n(n+1)/2 cards needed to restore them to their original order.at n=21A048782
• Triangle of number of permutations of {1, 2, ..., n} having exactly k cycles, each of which is of length >=r for r=3.at n=14A050211
• Expansion of e.g.f. (1-x)/(1 - 2*x - x^2 + x^3).at n=6A052559
• Expansion of e.g.f.: (1+2*x-2*x^2)/(1-x)^2.at n=7A052572
• E.g.f. (1-x)/(1-x-2x^3).at n=7A052601
• a(n) = n!*Pell(n) (or n!*A000129(n)).at n=6A052631
• E.g.f. (1+x-x^2)^2/(1-x)^2.at n=7A052643
• A simple context-free grammar in a labeled universe: labeled version of A049140.at n=6A052740
• Expansion of e.g.f.: x^3*(exp(x)-1)^3.at n=8A052784
• Numbers with an increasing number of nonprime divisors.at n=31A059992
• Consider the subsets of proper divisors of a number that sum to the number. These are numbers that set a record number of such subsets.at n=24A065218
• a(n) = A062401(A065391(n)): phi(sigma(m)) peak values for numbers m (listed in A065391) at which those peaks are first reached.at n=27A065392