110410

Appears in sequences

• A problem of configurations: a(0) = 1; for n>0, a(n) = (2n-1)!! - Sum_{k=1..n-1} (2k-1)!! a(n-k). Also the number of shellings of an n-cube, divided by 2^n n!.at n=7A000698
• Triangular matrix T, read by rows, that satisfies: SHIFT_LEFT(column 0 of T^((2*p-1)/2)) = (2*p-1)*(column p of T), or [T^((2*p-1)/2)](m,0) = (2*p-1)*T(p+m,p+1) for all m>=1 and p>=0.at n=21A105615
• Matrix square-root of triangle A105615.at n=29A105623
• Triangle, read by rows, defined by: T(n,k) = Sum_{j=0..n-k-1} T(j+k,k)*T(n-j,k+1) for n > k >= 0, with T(n,n) = n+1.at n=21A127058
• a(n) = 625*n^2 - 886*n + 314.at n=13A157618
• A(n,k) is the sum over all Dyck paths of semilength n of products over all peaks p of (x_p+k*y_p)/y_p, where x_p and y_p are the coordinates of peak p; square array A(n,k), n>=0, k>=0, read by antidiagonals.at n=34A258219
• A(n,k) is the sum over all Dyck paths of semilength n of products over all peaks p of (k*x_p+y_p)/y_p, where x_p and y_p are the coordinates of peak p; square array A(n,k), n>=0, k>=0, read by antidiagonals.at n=34A258222
• Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.at n=21A286781
• Array of sequences read by descending antidiagonals, row A(n) is Stieltjes generated from the sequence n, n+1, n+2, n+3, ....at n=38A321964
• Square table, read by antidiagonals: the g.f. for row n is given recursively by (2*n-1)*x*R(n,x) = 1 + (2*n-3)*x - 1/R(n-1,x) for n >= 1 with the initial value R(0,x) = Sum_{k >= 0} A112934(k+1)*x^k.at n=34A355721
• Numbers k such that the equation x^2 - k*y^4 = -1 has a solution for which |y| > 2.at n=36A356488
• Triangle read by rows. Number of perfect matchings by number of connected components.at n=29A362308
• a(n) = binomial(n+3, 4) + binomial(n+1, 3) + 1.at n=38A368881