20370

Appears in sequences

• Poincaré series [or Poincare series] for depths of roots in a certain root system.at n=12A019525
• a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2, a(2)=1, and a(3)=3.at n=12A024741
• Least k such that the first k terms of A006928 contain n more 2's than 1's.at n=11A025507
• Number of n-move king paths on 8 X 8 board from given corner to opposite corner.at n=10A025597
• a(n) = Sum_{d|n and gcd(d, n/d)=1} binomial(n,d).at n=19A056190
• a(n) = 2*(n-1)*(n^2 + 1).at n=21A071233
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 0), (0, -1, 1), (0, 1, 1), (1, 0, -1)}.at n=9A148940
• Triangle read by rows: T(n,k) = t(n,k) + t(n,n-k), where t(n,k) = 2*(n!/k!)*(2*(n + k) - 1).at n=31A154987
• Triangle read by rows: T(n,k) = t(n,k) + t(n,n-k), where t(n,k) = 2*(n!/k!)*(2*(n + k) - 1).at n=32A154987
• Triangle read by rows: T(n, k) = binomial(3*n, k-1) + binomial(3*n, n-k).at n=22A156003
• Triangle read by rows: T(n, k) = binomial(3*n, k-1) + binomial(3*n, n-k).at n=26A156003
• Irregular array T(n,k), read by rows: row n is the polynomial expansion in t of p(x,t) = exp(t*x)/(1 - x/t - t^4 * x^4) with weighting factors t^n*n!.at n=57A158777
• a(n) = (n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120.at n=20A161701
• Coefficient triangle of the numerators of the (n-th convergents to) the continued fraction 1/(w+2/(w+3/(w+4/... .at n=71A180049
• Number of nonnegative solutions to x^3 + y^3 + z^3 <= n^3.at n=30A224215
• G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n / (A(x)^2 - x)^(2*n+1) * [ Sum_{k=0..n} C(n,k)^2 * x^k * A(x)^(n-2*k) ]^2.at n=20A258053
• Indices in A006928 where the imbalance between 1's and 2's sets a new record.at n=24A274775
• G.f. A(x,y) satisfies: A( x - y*G(x,y), y) = x + (1-y)*G(x,y) such that G(x,y) = Integral A(x,y) dx, where the coefficients T(n,k) of x^n*y^k form a triangle read by rows n>=1, for k=0..n-1.at n=30A277410
• Numbers that are equal to the product of the numerator and denominator of the harmonic mean of their divisors.at n=12A348828
• Expansion of e.g.f. 1/(1 + LambertW(-x^3 * exp(x))).at n=7A362703