-3003

Appears in sequences

• Coefficient array for certain polynomials N(3; k,x) (rising powers of x).at n=34A062746
• Triangle of coefficients of characteristic polynomial of M_n, the n X n matrix M_(i,j) = min(i,j).at n=60A076756
• Riordan array (1/(1+x)^3,x/(1+x)^2).at n=49A109954
• Inverse of twin-prime related triangle A111125.at n=30A113187
• Expansion of c(x*y*(1-x)), c(x) the g.f. of A000108.at n=43A115179
• Triangle read by rows: T(0,0)=1; T(n,k) is the coefficient of x^(n-k) in the monic characteristic polynomial of the n X n matrix (min(i,j)) (i,j=1,2,...,n) (0 <= k <= n, n >= 1).at n=60A123970
• Triangle read by rows: T(0,0)=1; T(n,k) is the coefficient of x^(n-k) in the monic characteristic polynomial of the n X n matrix (min(i,j)) (i,j=1,2,...,n) (0 <= k <= n, n >= 1).at n=69A123970
• Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n band matrix with main diagonal 2,3,3,..., subdiagonal -3,-3,-3,..., sub-subdiagonal 1,1,1,... and superdiagonal -1,-1,-1,... (0<=k<=n).at n=39A124019
• Riordan array (1/(1+x), x/(1+x)^2), inverse array is A039599.at n=60A129818
• Triangular table of numerators of the coefficients of Laguerre-Sonin polynomials L(1/2,n,x).at n=22A131440
• 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 t_n(x), used to define continuous and n times differentiable sigmoidal transfer functions.at n=22A144815
• a(n) = - 12*a(n-1) - 54*a(n-2) - 112*a(n-3) - 105*a(n-4) - 36*a(n-5) - 2*a(n-6) with a(0)=a(1)=a(2)=0, a(3)=-3, a(4)=24, a(5)=-135.at n=7A215636
• Coefficient triangle for powers of x^2 of polynomials appearing in a generalized Melham conjecture on alternating sums of third powers of Chebyshev's S polynomials with odd indices. Coefficients in powers of x^2 of 2 + (-1)^n*S(2*n,x).at n=60A220670
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 345", based on the 5-celled von Neumann neighborhood.at n=29A271296
• First term of n-th difference sequence of (floor(r*k)), r = log(3), k >= 0.at n=15A325752
• G.f. A(x) satisfies: A(x) = x + x^2 / exp(A(x) + A(x^2)/2 + A(x^3)/3 + A(x^4)/4 + ...).at n=20A345232
• T(n,k) are the numerators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows.at n=42A356205