-30240

Appears in sequences

• Generalized Stirling number triangle of first kind.at n=15A051338
• Triangle of nonzero coefficients of Hermite polynomials H_n(x) in increasing powers of x.at n=30A059343
• Triangle read by rows. T(n, k) are the coefficients of the Hermite polynomial of order n, for 0 <= k <= n.at n=55A060821
• Hermite numbers.at n=10A067994
• 2n-th derivative of the Gaussian exp(-x^2) evaluated at x=0.at n=5A097388
• Infinite square array read by antidiagonals: T(m, 0) = 1, T(m, 1) = m; T(m, k) = (m - k + 1) T(m+1, k-1) - (k-1) (m+1) T(m+2, k-2).at n=43A105937
• A scaled Hermite triangle.at n=55A112227
• Inverse of triangle related to Padé approximation of exp(x).at n=49A119275
• Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(1,n).at n=7A126962
• Infinite square array read by antidiagonals: Q(m, 0) = 1, Q(m, 1) = 1; Q(m, 2k) = (m - 2k + 1)*Q(m+1, 2k-1) - (2k-1)*Q(m+2,2k-2), m*Q(m, 2k+1) = (m - 2k)*Q(m+1, 2k) - 2k(m+1)*Q(m+2, 2k-1).at n=65A127080
• Define an array by Q(m, 0) = 1, Q(m, 1) = 1; Q(m, 2k) = (m - 2k + 1)*Q(m+1, 2k-1) - (2k-1)*Q(m+2, 2k-2), m*Q(m, 2k+1) = (m - 2k)*Q(m+1, 2k) - 2k(m+1)*Q(m+2, 2k-1). Sequence gives Q(0,n).at n=10A127137
• Irregular triangle of coefficients of a partition transform for direct Lagrange inversion of an o.g.f., complementary to A134685 for an e.g.f.; normalized by the factorials, these are signed, refined face polynomials of the associahedra.at n=12A133437
• A triangular sequence based on concepts of operations on existing sequences: in this case the H(x,n) ( A060821) traditional Hermite is differentiated twice : p(x,n)=-x^2*H''(x,n)+H(x,n).at n=55A137449
• Triangular sequence of coefficients from the expansion of the derivative of the Bernoulli polynomial function: p(x,t) = t*exp(x*t)/(exp(t)-1); q(x,t) = p'(x,t) = dp(x,t)/dt.at n=26A137777
• Triangle of coefficients associate with the expansion of the K_3 graph matric characteristic polynomial as a Sheffer sequence: M = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}} f(t)=-t^3+3t+2 p(x,t)=Exp[x,t)/(2*t^3+3*t^2-1)=exp(x*t)(t^3*f(1/t)).at n=30A137943
• Irregular triangle from the expansion of p(x,t) = exp(x*t)/(x - t/2 - t/(exp(t) - 1)).at n=47A138169
• Triangle of the RBS1 polynomial coefficients.at n=20A160485
• Triangle read by rows, based on expansion of (x^2/(exp(x)-1))^m = x^m+sum(n>m T(n,m)*m!/((n-m)!*n!)*x^n).at n=37A191578
• The 10th Hermite Polynomial evaluated at n: H_10(n) = 1024*n^10 - 23040*n^8 + 161280*n^6 - 403200*n^4 + 302400*n^2 - 30240.at n=0A247855
• Expansion of e.g.f. (1 + x)^3*log(1 + x).at n=10A274266