Sequences

392,541 sequences

Inverse Euler transform of {1, primes}.A030011
Inverse Euler transform of {1, primes}.
Euler transform of {1, primes}.A030012
Euler transform of {1, primes}.
Moebius transform of {1, primes}.A030013
Moebius transform of {1, primes}.
Inverse Moebius transform of {1, primes}.A030014
Inverse Moebius transform of {1, primes}.
Binomial transform of {1, primes}.A030015
Binomial transform of {1, primes}.
Inverse binomial transform of {1, primes}.A030016
Inverse binomial transform of {1, primes}.
a(1) = 1, a(n+1) = Sum_{k = 1..n} p(k)*a(n+1-k), where p(k) is the k-th prime.A030017
a(1) = 1, a(n+1) = Sum_{k = 1..n} p(k)*a(n+1-k), where p(k) is the k-th prime.
Coefficients in 1/(1+P(x)), where P(x) is the generating function of the primes.A030018
Coefficients in 1/(1+P(x)), where P(x) is the generating function of the primes.
Number of labeled spanning trees in the complete hypergraph on n vertices (all hyperedges having cardinality 2 or greater).A030019
Number of labeled spanning trees in the complete hypergraph on n vertices (all hyperedges having cardinality 2 or greater).
Theta series of hypothetical extremal 16-dimensional strongly 6-modular lattice.A030020
Theta series of hypothetical extremal 16-dimensional strongly 6-modular lattice.
Theta series of 8-dimensional extremal strongly 10-modular lattice.A030021
Theta series of 8-dimensional extremal strongly 10-modular lattice.
Theta series of 8-dimensional extremal strongly 10-modular lattice.A030022
Theta series of 8-dimensional extremal strongly 10-modular lattice.
Theta series of 12-dimensional extremal strongly 10-modular lattice.A030023
Theta series of 12-dimensional extremal strongly 10-modular lattice.
Theta series of hypothetical extremal 16-dimensional strongly 10-modular lattice.A030024
Theta series of hypothetical extremal 16-dimensional strongly 10-modular lattice.
Theta series of 8-dimensional extremal 13-modular lattice.A030025
Theta series of 8-dimensional extremal 13-modular lattice.
Theta series of 12-dimensional extremal 15-modular lattice.A030026
Theta series of 12-dimensional extremal 15-modular lattice.
From average theta series of genus of 8-dimensional 17-modular lattices.A030027
From average theta series of genus of 8-dimensional 17-modular lattices.
Theta series of hypothetical extremal 12-dimensional strongly 21-modular lattice.A030028
Theta series of hypothetical extremal 12-dimensional strongly 21-modular lattice.
Theta series of hypothetical extremal 12-dimensional strongly 21-modular lattice.A030029
Theta series of hypothetical extremal 12-dimensional strongly 21-modular lattice.
Weight distribution of nonlinear binary (36,2^18,8) code.A030030
Weight distribution of nonlinear binary (36,2^18,8) code.
Binomial((n+1)^2, prime(n)).A030031
Binomial((n+1)^2, prime(n)).
a(n+1) = Sum_{k=0..floor(n/3)} a(k) * a(n-k).A030032
a(n+1) = Sum_{k=0..floor(n/3)} a(k) * a(n-k).
a(n+1) = Sum_{k = 0..floor(2*n/3)} a(k)*a(n-k) for n >= 0 with a(0) = 1.A030033
a(n+1) = Sum_{k = 0..floor(2*n/3)} a(k)*a(n-k) for n >= 0 with a(0) = 1.
a(n+1) = Sum_{k=0..floor(n/4)} a(k) * a(n-k).A030034
a(n+1) = Sum_{k=0..floor(n/4)} a(k) * a(n-k).
a(n+1) = Sum_{k=0..floor(3*n/4)} a(k) * a(n-k).A030035
a(n+1) = Sum_{k=0..floor(3*n/4)} a(k) * a(n-k).
a(n+1) = Sum_{k=0..floor(n/5)} a(k) * a(n-k).A030036
a(n+1) = Sum_{k=0..floor(n/5)} a(k) * a(n-k).
a(n+1) = Sum_{k=0..floor(2*n/5)} a(k) * a(n-k).A030037
a(n+1) = Sum_{k=0..floor(2*n/5)} a(k) * a(n-k).
a(n+1) = Sum_{k=0..floor(3*n/5)} a(k) * a(n-k).A030038
a(n+1) = Sum_{k=0..floor(3*n/5)} a(k) * a(n-k).
a(n+1) = Sum_{k=0..floor(4*n/5)} a(k) * a(n-k).A030039
a(n+1) = Sum_{k=0..floor(4*n/5)} a(k) * a(n-k).
a(n+1) = Sum_{k=0..floor(n/tau)} a(k) * a(n-k), where tau = (1+sqrt(5))/2.A030040
a(n+1) = Sum_{k=0..floor(n/tau)} a(k) * a(n-k), where tau = (1+sqrt(5))/2.
a(n+1) = Sum_{k=0..sqrt(n)} a(k) * a(n-k).A030041
a(n+1) = Sum_{k=0..sqrt(n)} a(k) * a(n-k).
Unreduced numerator of volume of best symplectic packing of n balls in 4-dimensional ball.A030042
Unreduced numerator of volume of best symplectic packing of n balls in 4-dimensional ball.
Unreduced denominator of volume of best symplectic packing of n balls in 4-dimensional ball.A030043
Unreduced denominator of volume of best symplectic packing of n balls in 4-dimensional ball.
High temperature series in v^2 = tanh(J/kT)^2 for spin-1/2 Ising partition function on 4D simple cubic lattice, divided by 2/(1+v)^4.A030044
High temperature series in v^2 = tanh(J/kT)^2 for spin-1/2 Ising partition function on 4D simple cubic lattice, divided by 2/(1+v)^4.
Low temperature series for spin-1/2 Ising partition function on 4D simple cubic lattice.A030045
Low temperature series for spin-1/2 Ising partition function on 4D simple cubic lattice.
Low temperature series for spin-1/2 Ising magnetic susceptibility on 4D simple cubic lattice (divided by 4).A030046
Low temperature series for spin-1/2 Ising magnetic susceptibility on 4D simple cubic lattice (divided by 4).
Low temperature series for spin-1/2 Ising partition function on 5D simple cubic lattice.A030047
Low temperature series for spin-1/2 Ising partition function on 5D simple cubic lattice.
High temperature series for spin-1/2 Ising partition function on 5D simple cubic lattice.A030048
High temperature series for spin-1/2 Ising partition function on 5D simple cubic lattice.
High temperature series for spin-1/2 Ising partition function on 6D simple cubic lattice.A030049
High temperature series for spin-1/2 Ising partition function on 6D simple cubic lattice.
Numbers from the Conway-Schneeberger 15-theorem.A030050
Numbers from the Conway-Schneeberger 15-theorem.
Numbers from the 290-theorem.A030051
Numbers from the 290-theorem.
Smallest number whose n-th power is a sum of distinct smaller positive n-th powers.A030052
Smallest number whose n-th power is a sum of distinct smaller positive n-th powers.
a(n) = binomial(2n+1,n-3).A030053
a(n) = binomial(2n+1,n-3).
a(n) = binomial(2n+1,n-4).A030054
a(n) = binomial(2n+1,n-4).
a(n) = binomial(2*n+1, n-5).A030055
a(n) = binomial(2*n+1, n-5).
a(n) = binomial(2*n+1, n-6).A030056
a(n) = binomial(2*n+1, n-6).
Least number that is not a sum of distinct divisors of n.A030057
Least number that is not a sum of distinct divisors of n.
Least non-sum of divisors of n for some n >= 1.A030058
Least non-sum of divisors of n for some n >= 1.
Numbers that are the product of an odd number of distinct primes.A030059
Numbers that are the product of an odd number of distinct primes.
Third derivative of Catalan generating function/3!.A030060
Third derivative of Catalan generating function/3!.