Sequences

392,541 sequences

Number of permutations of [n] with n-4 sequences.A001760
Number of permutations of [n] with n-4 sequences.
a(n) = (2*n)!/(n+1)!.A001761
a(n) = (2*n)!/(n+1)!.
Number of labeled n-vertex dissections of a ball.A001762
Number of labeled n-vertex dissections of a ball.
a(n) = (3n+3)!/(2n+3)!.A001763
a(n) = (3n+3)!/(2n+3)!.
a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).A001764
a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).
Coefficients of iterated exponentials.A001765
Coefficients of iterated exponentials.
Index of (the image of) the modular group Gamma(n) in PSL_2(Z).A001766
Index of (the image of) the modular group Gamma(n) in PSL_2(Z).
Genus of modular group Gamma(n) = genus of modular curve Chi(n).A001767
Genus of modular group Gamma(n) = genus of modular curve Chi(n).
Sorting numbers: number of comparisons for merge insertion sort of n elements.A001768
Sorting numbers: number of comparisons for merge insertion sort of n elements.
Expansion of 1/((1+x)*(1-x)^7).A001769
Expansion of 1/((1+x)*(1-x)^7).
Numbers k such that 5*2^k - 1 is prime.A001770
Numbers k such that 5*2^k - 1 is prime.
Numbers k such that 7*2^k - 1 is prime.A001771
Numbers k such that 7*2^k - 1 is prime.
Numbers k such that 11*2^k - 1 is prime.A001772
Numbers k such that 11*2^k - 1 is prime.
Numbers k such that 13*2^k - 1 is prime.A001773
Numbers k such that 13*2^k - 1 is prime.
Numbers k such that 17*2^k - 1 is prime.A001774
Numbers k such that 17*2^k - 1 is prime.
Numbers k such that 19*2^k - 1 is prime.A001775
Numbers k such that 19*2^k - 1 is prime.
Dimensions of the Jordan operad.A001776
Dimensions of the Jordan operad.
Lah numbers: a(n) = n! * binomial(n-1, 4)/5!.A001777
Lah numbers: a(n) = n! * binomial(n-1, 4)/5!.
Lah numbers: a(n) = n!*binomial(n-1,5)/6!.A001778
Lah numbers: a(n) = n!*binomial(n-1,5)/6!.
Expansion of 1/((1+x)(1-x)^8).A001779
Expansion of 1/((1+x)(1-x)^8).
Expansion of 1/((1+x)*(1-x)^9).A001780
Expansion of 1/((1+x)*(1-x)^9).
Expansion of 1/((1+x)*(1-x)^10).A001781
Expansion of 1/((1+x)*(1-x)^10).
Discriminants of Shapiro polynomials.A001782
Discriminants of Shapiro polynomials.
n-phi-torial, or phi-torial of n: Product k, 1 <= k <= n, k relatively prime to n.A001783
n-phi-torial, or phi-torial of n: Product k, 1 <= k <= n, k relatively prime to n.
Second-order reciprocal Stirling number (Fekete) a(n) = [[2n+3, n]]. The number of n-orbit permutations of a (2n+3)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g., Comtet).A001784
Second-order reciprocal Stirling number (Fekete) a(n) = [[2n+3, n]]. The number of n-orbit permutations of a (2n+3)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g., Comtet).
Second-order reciprocal Stirling number (Fekete) a(n) = [[2n+4, n]]. The number of n-orbit permutations of a (2n+4)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g., Comtet).A001785
Second-order reciprocal Stirling number (Fekete) a(n) = [[2n+4, n]]. The number of n-orbit permutations of a (2n+4)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g., Comtet).
Expansion of 1/((1+x)*(1-x)^11).A001786
Expansion of 1/((1+x)*(1-x)^11).
a(n) = n*2^(n-1).A001787
a(n) = n*2^(n-1).
a(n) = n*(n+1)*2^(n-2).A001788
a(n) = n*(n+1)*2^(n-2).
a(n) = binomial(n,3)*2^(n-3).A001789
a(n) = binomial(n,3)*2^(n-3).
Numerators in expansion of 1/sqrt(1-x).A001790
Numerators in expansion of 1/sqrt(1-x).
a(n) = binomial coefficient C(2n, n-1).A001791
a(n) = binomial coefficient C(2n, n-1).
a(n) = (n+2)*2^(n-1).A001792
a(n) = (n+2)*2^(n-1).
a(n) = n*(n+3)*2^(n-3).A001793
a(n) = n*(n+3)*2^(n-3).
Negated coefficients of Chebyshev T polynomials: [x^n](-T(n+6, x)), n >= 0.A001794
Negated coefficients of Chebyshev T polynomials: [x^n](-T(n+6, x)), n >= 0.
Coefficients of Legendre polynomials.A001795
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001796
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001797
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001798
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001799
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001800
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001801
Coefficients of Legendre polynomials.
Coefficients of Legendre polynomials.A001802
Coefficients of Legendre polynomials.
Numerators in expansion of (1 - x)^(-3/2).A001803
Numerators in expansion of (1 - x)^(-3/2).
a(n) = n! * C(n,2).A001804
a(n) = n! * C(n,2).
a(n) = n! * binomial(n,3).A001805
a(n) = n! * binomial(n,3).
a(n) = n! * binomial(n,4).A001806
a(n) = n! * binomial(n,4).
a(n) = n! * binomial(n,5).A001807
a(n) = n! * binomial(n,5).
Expansion of 1/((1+x)*(1-x)^12).A001808
Expansion of 1/((1+x)*(1-x)^12).
a(n) = n! * n(n-1)/4.A001809
a(n) = n! * n(n-1)/4.