27940

Appears in sequences

• Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n, having k long ascents (i.e., ascents of length at least 2). Rows are of length 1,1,2,2,3,3,... .at n=39A091156
• Riordan array (1/(1-x*c(3*x)), x*c(3*x)/(1-x*c(3*x))), c(x) the g.f. of A000108.at n=40A110519
• Triangle read by rows: T(n,k) is the number of 2-Motzkin paths (i.e., Motzkin paths with blue and red level steps) without red level steps on the x-axis, having length n and k level steps (0 <= k <= n).at n=71A126222
• Triangle read by rows: a(n,k) = number of permutations in S_n which avoid the pattern 123 and have exactly k descents.at n=63A166073
• Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.at n=25A187608
• Expansion of ((x-1)*sqrt(1-4*x^2))/((x-1)*sqrt(1-4*x^2)+x).at n=12A190788
• a(n) = A005291(n) + A005291(n+1).at n=35A195308
• Poincaré series for invariant polynomial functions on the space of binary forms of degree 16.at n=19A293941
• Number of Sophie Germain primes of the form 4k + 1 less than 10^n.at n=6A307176
• Lesser of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A380845(k) - k is the sum of aliquot divisors of k that have the same binary weight as k.at n=0A380849