-468

Appears in sequences

• a(n) = (2^n/n!) * Product_{k=0..n-1} (4*k - 3).at n=5A004983
• Expansion of Product_{k>=1} (1 - x^k)^9.at n=40A010817
• Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^6.at n=11A029843
• Expansion of cube of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).at n=23A055102
• Signed generalized Fibonacci numbers.at n=5A080244
• Riordan array ((1-x^2)/(1+3x+x^2),x/(1+3x+x^2)).at n=24A110168
• G.f.: (x^3+6*x+2)^2/(x^2+x+1)^2.at n=51A115054
• G.f.: (x^3+6*x+2)^2/(x^2+x+1)^2.at n=53A115054
• a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the n-th prime.at n=20A117330
• Triangle read by rows: characteristic polynomials of certain matrices, see Mathematica program.at n=24A124040
• Said to have been posted at the web site mturk.amazon.com as a puzzle.at n=9A124170
• a(n) = A062295(n) - A133743(n).at n=39A133744
• Triangle T(n, k) = Product_{j=1..k} Product_{i=0..j-1} ( 1 - (n-k+1)*(i+1) ) with T(n, 0) = 1 and T(n, n) = n!, read by rows.at n=38A156693
• E.g.f. satisfies: A(x) = (1+x)/(1+3*x) * A(x*(1+x)^2).at n=4A179330
• a(n) = 13*a(n-1) - 65*a(n-2) + 156*a(n-3) - 182*a(n-4) + 91*a(n-5) - 13*a(n-6).at n=3A216801
• Expansion of (phi(q)^4 + 7 * phi(-q)^4) / 8 in powers of q where phi() is a Ramanujan theta function.at n=45A228745
• Difference between sums of quadratic residues and non-residues modulo n that are coprime to n.at n=77A255643
• Expansion of phi(-x^2)^6 * psi(x^6) / f(x)^2 in powers of x where phi(), psi(), f() are Ramanujan theta functions.at n=29A263398
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 150", based on the 5-celled von Neumann neighborhood.at n=23A270324
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 597", based on the 5-celled von Neumann neighborhood.at n=25A273147