Sequences

Nearest integer to imaginary part of n-th zero of Riemann zeta function.

Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.

Hexagonal pyramidal numbers, or greengrocer's numbers.

Heptagonal (or 7-gonal) pyramidal numbers: a(n) = n*(n+1)*(5*n-2)/6.

Octagonal pyramidal numbers: a(n) = n*(n+1)*(2*n-1)/2.

4-dimensional pyramidal numbers: a(n) = n^2*(n^2-1)/12.

a(n) = 2^(n^2).

4-dimensional figurate numbers: a(n) = n*binomial(n+2, 3).

4-dimensional figurate numbers: a(n) = (5*n-1)*binomial(n+2,3)/4.

4-dimensional figurate numbers: a(n) = (6*n-2)*binomial(n+2,3)/4.

Expansion of sqrt(1 - 4*x) in powers of x.

Expansion of (1-4*x)^(3/2) in powers of x.

Expansion of (1-4*x)^(5/2).

Expansion of (1-4*x)^(7/2).

Expansion of (1-4*x)^(9/2).

Denominator of Pi^(2n)/(Gamma(2n)*(1-2^(-2n))*zeta(2n)).

Central trinomial coefficients: largest coefficient of (1 + x + x^2)^n.

Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

Numerators of coefficients of expansion of arctan(x)^2 = x^2 - 2/3*x^4 + 23/45*x^6 - 44/105*x^8 + 563/1575*x^10 - 3254/10395*x^12 + ...

Numerators of double sums of reciprocals.

Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x).

Numerators in Taylor series for cot x.

Denominators of zeta(2*n)/Pi^(2*n).

Theta series of unique 26-dimensional unimodular lattice T_26 with no roots (and minimal norm 3).

Theta series of Borcherds' 27-dimensional unimodular lattice T_27.

Second-order Euler numbers.

E.g.f.: Sum_{n >= 0} a(n)*x^(2*n)/(2*n)! = sec(2*x).

a(n) = A000364(n) * (3^(2*n+1) + 1)/4.

Multiples of Euler numbers.

Glaisher's T numbers.

Squares written in base 7.

Squares written in base 8.

Squares written in base 9.

Numerator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.

Denominator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.

Denominators of Bernoulli numbers B_{2n}.

a(n) = 2^(2*n+1) - 2.

Expansion of 1/(1-2*x^2-3*x^3).

Expansion of Jacobi theta function theta_4(x).

Number of different types of binary trees of height n.

a(n) = (4^n - 1)/3.

Expansion of 1/((1-x)*(1-4*x)*(1-9*x)).

a(n) = (9^n - 1)/8.

Central factorial numbers: 2nd subdiagonal of A008958.

Central factorial numbers: a(n) = 4^n * (n!)^2.

Central factorial numbers: unsigned 1st subdiagonal of A182867.

Joffe's central differences of 0, A241171(n,n-1).

a(n) = (2n+1)!/n!^2.

a(n) = binomial(4*n+1, 2*n).

Nearest integer to cosh(n).