-488

Appears in sequences

• arcsinh(tan(x)*exp(x)) = x+2/2!*x^2+4/3!*x^3-60/5!*x^5-488/6!*x^6...at n=6A012362
• E.g.f. arctan(sec(x)*sinh(x)) (odd powers only).at n=3A012816
• Dirichlet inverse of sigma_2 function (A001157).at n=43A053822
• McKay-Thompson series of class 22B for Monster.at n=29A058568
• Expansion of (x - 1)/(1 - x^2 + x^3 + x^4 - x^5).at n=59A115413
• Expansion of E(k) * K(k) * (2/Pi)^2 in powers of q^2 where E(), K() are complete elliptic integrals and the nome q = exp( -Pi * K(k') / K(k)).at n=32A122858
• McKay-Thompson series of class 22B for the Monster group with a(0) = -2.at n=29A132320
• Triangle read by rows: row n gives coefficients of increasing powers of x in the polynomial (-1)^n*p(n), where p(n) is defined as follows. Let f(n) = n*(n+1)/2, g(n) = f(n)+1; then p(-1) = 0, p(0) = 1 and for n >= 1, p(n) = (x - f(n))*p(n - 1) - g(n - 1)^2*p(n - 2).at n=17A135049
• Expansion of K(k) * (2 * E(k) - K(k)) / (Pi/2)^2 in powers of q where E(k), K(k) are complete elliptic integrals and q = exp(-Pi * K(k') / K(k)).at n=32A143336
• Expansion of q^(1/4) * eta(q^5)^2 * eta(q^20) / (eta(q^4) * eta(q^10)^2) in powers of q.at n=65A146165
• Diagonal sums of the Riordan array (1-4*x+4*x^2, x*(1-2*x)) (A167431).at n=13A167434
• Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A115255 (in square format); by antidiagonals.at n=12A203005
• a(n) = (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4) with a(0) = 1, a(1) = 1, a(2) = 0, a(3) = 1, a(6) = 2.at n=18A247370
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 141", based on the 5-celled von Neumann neighborhood.at n=13A270285
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 214", based on the 5-celled von Neumann neighborhood.at n=47A270908
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 262", based on the 5-celled von Neumann neighborhood.at n=33A271068
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 414", based on the 5-celled von Neumann neighborhood.at n=48A272015
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 534", based on the 5-celled von Neumann neighborhood.at n=31A272789
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 710", based on the 5-celled von Neumann neighborhood.at n=29A273424
• Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = e - 1, s = r/(1-r).at n=18A279632