1028160

Appears in sequences

• a(n) = (3n+3)!/(2n+3)!.at n=6A001763
• a(n+1) = (n-1)*a(n) + n*n!.at n=7A006157
• Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x.at n=28A008294
• Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to complement, inequivalent to reverse and reversed complement.at n=20A045668
• A simple context-free grammar in a labeled universe: labeled version of A052708.at n=7A052738
• Product of 5 consecutive integers.at n=18A052787
• E.g.f.: x^5*exp(x)-x^5.at n=18A052800
• Triangle a(n,k) read by rows n which contain columns k=1,2,..,n, where each entry is the product of numbers (k-1)*n-T(k-2)+1 through k*n-T(k-1).at n=23A093447
• Triangle T(n,k), 0 <= k <= n, read by rows, defined by T(0,0) = 1; T(0,k) = 0 if k>0 or if k<0; T(n,k) = k*T(n-1,k-1) + (k+1)*T(n-1,k+1).at n=52A104035
• The r-th term of the n-th row of the following triangle contains product of r successive numbers in decreasing order beginning from T(n)-T(r-1) where T(n) is the n-th triangular number. 1 3 2 6 20 6 10 72 210 24 15 182 1320 3024 120 ... Sequence contains the triangle by rows.at n=25A110768
• Triangle read by rows: T[n,k] = the number of ascending runs of length at least k in the permutations of [n] for k <= n.at n=37A122844
• a(1)=1. a(n+1) = n!/lcm(a(1),a(2),...,a(n)).at n=17A131120
• Expansion of g.f. x*(1 - x)*(1 + x)/((x^2 + 3*x + 1)*(x^2 - 4*x + 1)).at n=12A171067
• Bi-unitary multiperfect numbers.at n=12A189000
• Triangle read by rows, k!*2^k*S_2(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0.at n=42A225476
• Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.at n=25A249253
• Highly composite numbers of class 5 (see comment in A275239).at n=34A275243
• Triangle T(n,k) (n>=0, 0<=k<=n) read by rows: T(0,0)=T(1,1)=1; T(n,0) is the Euler number A000111(n-1) for n>=1; T(n,n-1) = T(n,n) = (n-2)! for n>=2; interior entries are given by T(n,k) = m*T(n-1,k-1)+(k+1)*T(n-1,k+1) where m = k if n+k is even or k-1 if n+k is odd.at n=62A350970
• Positions of records in A357299: integers m such that the number of divisors whose first digit equals the first digit of m sets a new record.at n=20A355592
• Numbers m such that A357761(m) < A357761(k) for all k < m.at n=27A357764