205056

Appears in sequences

• 5th forward differences of factorial numbers A000142.at n=4A001689
• Expansion of (1-x)/(1-2x-4x^2+4x^3).at n=12A052904
• Triangle T[n,m]: T[n,-1] = 0; T[0,0] = 0; T[n,0] = n*n!; T[n,m] = T[n,m-1] - T[n-1,m-1].at n=40A061312
• Euler's difference table: triangle read by rows, formed by starting with factorial numbers (A000142) and repeatedly taking differences. T(n,n) = n!, T(n,k) = T(n,k+1) - T(n-1,k).at n=49A068106
• Numbers k such that the concatenation of k with 4*k gives a square.at n=31A115535
• First differences of the rows in the triangle of A116853, starting with 0.at n=49A116854
• Number of permutations of {1,2,...,n} that have no odd fixed points.at n=9A161131
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having exactly k odd fixed points (0 <= k <= ceiling(n/2)).at n=29A161133
• G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum_{k=0..2*n} A200536(n,2*n-k)^2 * x^k] / A(x)^n * x^n/n ), where A200536(n,2*n-k) is the coefficient of x^k in (2+3*x+x^2)^n.at n=21A251689
• Fifth column of Euler's difference table in A068106.at n=8A277563
• a(n) = coefficient of x^n*y^(n+1)/n! in (1/2) * log( Sum_{n>=0} (n^2 + n*y + 2*y^2)^n * x^n/n! ).at n=5A359918