Sequences

Arrange the nontrivial binomial coefficients C(m,k) (2 <= k <= m/2) in increasing order (not removing duplicates); record the sequence of m's.

Arrange the nontrivial binomial coefficients C(m,k) (2 <= k <= m/2) in increasing order (not removing duplicates); record the sequence of k's.

Arrange the nontrivial binomial coefficients C(m,k) (2 <= k <= m-2) in increasing order; record the positions of the central binomial coefficients.

Multinomial coefficients(TOP, BOTTOM), where TOP = 2^n, BOTTOM = ( C(n,0) C(n,1) C(n,2) ... C(n,n) ).

Multinomial coefficients (0, 1, ..., n)! = C(n+1,2)!/(0!*1!*2!*...*n!).

Multinomial coefficient n!/([n/3]![(n+1)/3]![(n+2)/3]!).

Multinomial coefficient n!/ ([n/4]!, [(n+1)/4]!, [(n+2)/4]!, [(n+3)/4]!).

Multinomial coefficients(TOP, BOTTOM), where TOP = n(n+1)(2n+1)/6, BOTTOM = ( 1^2 2^2 ... n^2 ).

Multinomial coefficients(TOP, BOTTOM), where TOP = n^2, BOTTOM = ( 1 3 5 ... 2n-1 ).

Number of solutions to c(1)*prime(4) + ... + c(n)*prime(n+3) = 2, where c(i) = +-1 for i > 1, c(1) = 1.

Number of integers m such that 3^n < 2^m < 3^(n+1).

Number of integers m such that 5^n < 2^m < 5^(n+1).

Number of integers m such that 7^n < 2^m < 7^(n+1).

Number of 3^m between 2^n and 2^(n+1).

Number of 5^m between 2^n and 2^(n+1).

Number of powers of 7 between 2^n and 2^(n+1).

Number of integers m such that 5^n < 3^m < 5^(n+1).

Number of 5^m between 3^n and 3^(n+1).

Number of 3^m between 4^n and 4^(n+1).

Number of 4^m between 3^n and 3^(n+1).

Number of e^m between Pi^n and Pi^(n+1).

a(n) is the number of powers Pi^m between e^n and e^(n+1).

Number of e^m between 2^n and 2^(n+1).

Number of 2^m between e^n and e^(n+1).

a(n) = a(n-1) + c(n-1) for n >= 2, a( ) increasing, given a(1)=3, where c( ) is complement of a( ).

a(n) = a(n-1) + c(n-1) for n >= 2, a( ) increasing, given a(1)=4; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n-1) for n >= 2, a( ) increasing, given a(1)=5; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n-1) for n >= 2, a( ) increasing, given a(1)=6; where c( ) is complement of a( ).

Unique increasing sequence satisfying a(n) = a(n-2) + c(n-2); where c( ) is complement of a( ).

a(n) = a(n-1) + b(n-2) for n >= 3, a( ) increasing, given a(1) = 1, a(2) = 3; where b( ) is complement of a( ).

a(n) = a(n-1) + c(n-2) for n >= 3, a( ) increasing, given a(1)=1, a(2)=2; where c( ) is complement of a( ).

a(n) = a(n-2) + c(n-1) for n >= 3, a( ) increasing, given a(1)=1, a(2)=2; where c( ) is complement of a( ).

a(n) = a(n-2) + c(n-1) for n >= 3, a( ) increasing, given a(1)=2, a(2)=3, where c( ) is complement of a( ).

a(n) = a(n-2) + c(n-1) for n >= 3, a( ) increasing, given a(1)=2, a(2)=4; where c( ) is complement of a( ).

Duplicate of A022443.

a(n) = a(n-1) + c(n) for n >= 3, a( ) increasing, given a(1)=1 a(2)=2; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n) for n >= 3, a( ) increasing, given a(1)=1 a(2)=3; where c( ) is complement of a( ).

Duplicate of A022443.

a(n) = a(n-1) + c(n) for n >= 3, a( ) increasing, given a(1)=1 a(2)=6; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n) for n >= 3, a( ) increasing, given a(1)=1 a(2)=7; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n) for n >= 3, a( ) increasing, given a(1)=2, a(2)=3; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n) for n >= 3, a( ) increasing, given a(1)=3 a(2)=6; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n+1) for n >= 3, a( ) increasing, given a(1)=1, a(2)=7; where c( ) is complement of a( ).

a(n) = a(n-1) + c(n+1) for n >= 3, a( ) increasing, given a(1)=1, a(2)=8; where c( ) is complement of a( ).

Unique increasing sequence satisfying a(n) = a(n-3) + c(n-3); where c( ) is complement of a( ).

Unique increasing sequence satisfying a(n) = a(n-4) + c(n-4); where c( ) is complement of a( ).

Unique increasing sequence satisfying a(n) = a(n-5) + c(n-5); where c( ) is complement of a( ).

a(n) = 2 - n.

a(n) = 3-n.

a(n) = 4-n.