-3360

Appears in sequences

• A scaled Hermite triangle.at n=38A112227
• Triangle of polynomials P(n,x) of degree n related to Pi (see comment) and derived from Padé approximation to exp(x).at n=18A113216
• Inverse of triangle related to Padé approximation of exp(x).at n=32A119275
• Irregular triangle read by rows: T(n,k) (n>=1, 0<=k<=n(n-1)/2) is such that Sum_k T(n,k)*p^(n*(n-1)/2-k) gives the expectation of the number of connected components after deleting every edge of the complete graph on n labeled vertices with probability p.at n=64A125209
• A triangular sequence of coefficients of an expansion of a Mach wave as a traveling wave in a medium: (vt')^2 = vp*vg = c^2 - (gamma-1)/(gamma+1)*vt^2; Substituting: vt -> exp(t*x); gamma->t; c->1; p(x,t) = 1 - exp(2*x*t)*(t - 1)/(1 + t).at n=32A138024
• Triangle a(n,k) of the expansion coefficients of the Hermite polynomial 2*H(n/2,x) if n even, of H((n-1)/2,x)+H((n+1)/2,x) if n odd.at n=64A139158
• A triangle of coefficients from Hermite polynomials A060821 as {x,y},{y,z},{z,x} binomials reduced to x: f(x,y,n)=Sum[Coefficients(H(x,n))(i)*x^i*y^(n-1),{i,0,n}]; p(x,y,z)=f(x,y,n)+f(y,z,n)+f(z,x,n).at n=29A139583
• Numerators of triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) is the coefficient of x^(2k+1) in polynomial v_n(x), used to approximate x->sin(Pi*x)/Pi.at n=11A144859
• S(n,k) an additive decomposition of the Springer number (generalized Euler number), (triangle read by rows).at n=19A154343
• Triangle T(n, k) = coefficients of p(n, x), where p(n, x) = (-1)^n*(x+2-n)*(x+2)^(n-1), p(0, x) = 1, and p(1, x) = -1-x, read by rows.at n=61A158285
• Triangle of successive recurrences in columns of A117317(n).at n=48A185342
• A triangle whose rows add up to the numerators of the Bernoulli numbers (with B(1) = 1/2). T(n, k) for n >= 0, 0 <= k <= n.at n=32A194587
• Triangle T(n,m) = coefficient of x^n in expansion of x^m*(x+1)^(m*x^2) = sum(n>=m, T(n,m) x^n*m!/n!).at n=31A202184
• n-th derivative of cosh(x)^sin(x) at x=0.at n=8A215583
• Expansion of (1 - t)*(1 + t)^x.at n=41A227342
• Coefficients for the commutator for the logarithm of the derivative operator [log(D),x^n D^n]=d[(xD)!/(xD-n)!]/d(xD) expanded in the operators :xD:^k.at n=30A238363
• Shifted lower triangular matrix A238363 with a main diagonal of ones.at n=38A238385
• a(n) = (-1)^n*(n+3)!/(2*(n+1)) for n >= 0.at n=5A238474
• a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>3, a(0)=a(1)=a(3)=0, a(2)=1.at n=18A240847
• Irregular triangle read by rows of normalized Girard-Waring formula (cf. A210258), for m=8 data values.at n=22A288188