111384

Appears in sequences

• Number of 5-tuples (p_1, p_2, ..., p_5) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.at n=5A006151
• Triangle of C(n+1,k)*C(2*n-3*k,n-3*k)/(n+1) by rows.at n=32A073187
• Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 2 simple intersections.at n=9A074922
• Upper triangle of Catalan Number Wall.at n=50A078920
• Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x) - x^2/(1-x)^3 + xy*f(x,y)^3.at n=42A086632
• From enumerating paths in the plane.at n=6A091962
• Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 33 for n > 0.at n=22A101526
• Triangle read by rows, where the g.f. satisfies A(x, y) = 1 + x*A(x, y)^2 + x*y*A(x, y)^3.at n=38A104978
• Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have k peaks of the form Ud.at n=42A108426
• Triangle read by rows, giving Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).at n=49A123352
• Triangle read by rows: T(n,k) is the number of ordered trees with n edges and 2k nodes of odd degree (not outdegree; 1 <= k <= ceiling(n/2)).at n=47A127157
• Sum of all parts of all partitions of n that do not contain 1 as a part.at n=35A138880
• Sum of parts in all partitions of 2n that do not contain 1 as a part.at n=18A182736
• Number of n X 5 binary arrays with every 1 having exactly three king-move neighbors equal to 1.at n=13A183452
• Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y<3z.at n=27A212520
• a(n) = 6*binomial(n+1, 6).at n=12A253946
• Number T(n,k) of modified skew Dyck paths of semilength n with exactly k anti-down steps; triangle T(n,k), n>=0, 0<=k<=n-floor((1+sqrt(max(0,8n-7)))/2), read by rows.at n=38A274404
• G.f.: 3F2([4/9, 5/9, 8/9], [2/3, 1], 729 x).at n=2A275459
• Consider all 3 X 3 matrices M whose entries are the n-th to (n+8)-th primes prime(n), ..., prime(n+8), in any order. a(n) is the sum of the number of M such that det(M) is divisible by prime(n+i), for i from 0 to 8.at n=6A339105
• Number of n-tuples (p_1, p_2, ..., p_n) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.at n=5A355400