70369

Appears in sequences

• A new general triangle sequence based on the Eulerian form in three parts ( subtraction):m=1; t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) + (m*k + 1)*t0(n - 1 + 1, k) - m*k*(n - k)*t0(n - 2 + 1, k - 1)].at n=39A157179
• A new general triangle sequence based on the Eulerian form in three parts ( subtraction):m=1; t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) + (m*k + 1)*t0(n - 1 + 1, k) - m*k*(n - k)*t0(n - 2 + 1, k - 1)].at n=41A157179
• Number of n X 8 binary arrays with all 1's connected, a path of 1's from top row to bottom row, and no 1 having more than two 1's adjacent.at n=3A163720
• Number of n X 4 binary arrays with all 1s connected, a path of 1s from left column to right column, and no 1 having more than two 1s adjacent.at n=7A163725
• Number of binary strings of length n with equal numbers of 00010 and 01011 substrings.at n=17A164217
• Zero together with the partial sums of A056640.at n=25A274772