127905

Appears in sequences

• Sum of squares of coefficients in full expansion of (z1+z2+...+zn)^n.at n=5A033935
• Third binomial transform of binomial(n+6, 6).at n=6A081905
• Coefficients of expansion of 1/sqrt(1 - 10*x + 9*x^2); also, a(n) is the central coefficient of (1 + 5*x + 4*x^2)^n.at n=6A084771
• The function W_n(10) (see Borwein et al. reference for definition).at n=4A169713
• The function W_5(2n) (see Borwein et al. reference for definition).at n=5A169714
• Let y = y(u,v) be implicitly defined by g(u,v,y(u,v)) = 0. Read as a triangle by rows, the sequence represents the number of terms a(i,k-i) in the expansion of the bivariate divided difference [u_0,...,u_i; v_0,...,v_{k-i}]y in terms of trivariate divided differences of g.at n=28A172003
• Let y = y(u,v) be implicitly defined by g(u,v,y(u,v)) = 0. Read as a triangle by rows, the sequence represents the number of terms a(i,k-i) in the expansion of the bivariate divided difference [u_0,...,u_i; v_0,...,v_{k-i}]y in terms of trivariate divided differences of g.at n=33A172003
• A(n,k) is the sum of k-th powers of coefficients in full expansion of (z_1+z_2+...+z_n)^n; square array A(n,k), n>=0, k>=0, read by antidiagonals.at n=33A245397
• Triangle read by rows: enumerates pairs of amicable permutations by rises.at n=24A259465
• Triangle read by rows: enumerates pairs of amicable permutations by rises.at n=26A259465
• Square array A(n,k) = (n!)^2 [x^n] BesselI(0, 2*sqrt(x))^k read by antidiagonals.at n=60A287316
• Square array read by descending antidiagonals: T(n, k) where column k is the expansion of 1/sqrt(1 - 2*(k+1)*x + ((k-1)*x)^2).at n=61A307883
• Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j * binomial(n,j) * binomial(2*j,j).at n=42A340970
• E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x^2/2)).at n=8A367754