8467200

Appears in sequences

• Sum of divisors of k such that k and k+1 have the same number and sum of divisors.at n=26A054005
• a(n) = n*(n+1)^2*(n+2)^3*(n+3)^2*(n+4).at n=4A057658
• Exponential transform of unsigned Lah-triangle |A008297(n,k)|.at n=38A079005
• Number of runs of length 1 in all permutations of [n]. (The permutation 3574162 has two runs of length 1: 357/4/16/2.)at n=9A097900
• n!*(3*n^2-13*n+14)/6.at n=7A108033
• Triangle read by rows: T(n,k) = the number of ascending runs of length k in the permutations of [n] for k <= n.at n=45A122843
• Irregular triangle read by rows: coefficients of Laplace transform of a Bernoulli expansion: LaplaceTransform[t*Exp[x*t]/(Exp[t] - 1), t, 1/t] = Zeta[2,1+1/t-x]->shifted to Zeta[4,1+1/t-x].at n=28A137496
• A triangular sequence of coefficients from a Laplace Transform of a Bernoulli expansion function: LaplaceTransform[t*Exp[x*t]/(Exp[t] - 1), t, 1/t] = Zeta[2,1+1/t-x]->shifted to Zeta[5,1+1/t-x].at n=22A137498
• A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)*StirlingS1[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].at n=24A156586
• The sixth row of the ED2 array A167560.at n=15A167563
• a(1)=1; a(n) = n*lcm(n, a(n-1)) for n > 1.at n=7A192217
• Number of stretching pairs in all permutations in S_n.at n=9A216119
• Triangle read by rows: T(n,k) (n>=1, 3<=k<=n+2) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are the same color as some other ball in the sequence.at n=50A292930
• Numbers k such that k and the next two numbers after k with the same prime signature as k also have the same set of distinct prime divisors as k.at n=30A340303
• Powerful numbers that have more divisors than any smaller powerful number.at n=38A377138
• Numbers k that have a record number of divisors that have the same binary weight as k.at n=30A381069
• Triangle read by rows: T(n, k) = (n! / (n - k)!) * Product_{k=1..n} radical(k), where radical(n) is the product of distinct prime factors of n, cf. A007947.at n=40A387126
• Numbers k such that there exist three numbers x, y and z such that k = psi(x) = psi(y) = psi(z) = x + y + z.at n=26A387290
• Triangle read by rows: T(n,k) = Sum_{j=0..2k} (-1)^j * binomial(2k,j) * (2+k-j)^(2n).at n=19A390029
• E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2 * (exp(x^2*A(x)) - 1).at n=10A392955