Sequences

Infinite square array f(a,b) = C(a+b,b+1)*(a*b+a+1)/(b+2), a, b >= 0, read by antidiagonals. Equivalently, triangular array T(n,k) = f(k,n-k), 0 <= k <= n, read by rows.

a(n) = n^3 + n.

a(n) = binomial(n+4,4)*(4*n+5)/5.

a(n) = f(n,4) where f is given in A034261.

a(n) = binomial(n+6,6)*(6*n+7)/7.

Partial sums of A027818.

a(n) = f(n,n) where f is given in A034261.

a(n) = LCM_{k=1..n} (2^k - 1).

a(n) = f(n,n+2) where f is given in A034261.

f(n,n+3) where f is given in A034261.

a(n) = f(n,n+4) where f is given in A034261.

a(n) = f(n,n+5) where f is given in A034261.

a(n) = binomial(2*n+6,n+7)*(n^2+7*n+1)/(n+8) = f(n,n+6) where f is given in A034261.

a(n)=f(n,n-1) where f is given in A034261.

a(n) = f(n,n-2) where f is given in A034261.

Smallest prime that generates a prime pyramid of height n.

Decimal part of a(n)^(1/2) starts with a 'nine digits' anagram.

Decimal part of a(n)^(1/3) starts with a 'nine digits' anagram.

Decimal part of a(n)^(1/4) starts with a 'nine digits' anagram.

Decimal part of a(n)^(1/5) starts with a 'nine digits' anagram.

Numbers k such that the decimal part of k^(1/6) starts with a 'nine digits' anagram.

Numbers k such that the decimal part of k^(1/7) starts with a 'nine digits' anagram.

Numbers k such that the decimal part of k^(1/8) starts with a 'nine digits' anagram.

Numbers k such that the decimal part of k^(1/9) starts with a 'nine digits' anagram.

Numbers k such that the decimal part of k^(1/10) starts with a 'nine digits' anagram.

Decimal part of n^(1/11) starts with a 'nine digits' anagram.

Numbers whose product of divisors is larger than that of any smaller number.

Product of proper divisors is larger than for any smaller number.

Squares which can be rearranged into squares with the same number of digits.

Cubes that have some nontrivial permutation of digits that is also a cube.

Triangular numbers that have some nontrivial permutation of digits which is also triangular.

Fibonacci numbers with exactly 2 different digits (probably finite).

Numbers k such that 2^k does not contain the digit 2 (probably finite).

Numbers k not ending in 0 such that for some base b, k_b is the reverse of k_10 (where k_b denotes k written in base b).

Number of different ways to divide an n X n square into sub-squares, considering only the list of parts.

Number of flat partitions of n: partitions {a_i} with each |a_i - a_{i-1}| <= 1.

Number of ordered positive integer solutions (m_1, m_2, ..., m_k) (for some k) to Sum_{i=1..k} m_i=n with |m_i-m_{i-1}| <= 1 for i = 2 ... k.

a(n) = min_S max_i b_i where S={b_i} (1 <= i <= n), b_i > 0, b_i distinct and either b_i|b_{i-1} or b_{i-1}|b_i.

Alternating sum transform (PSumSIGN) of A000975.

a(n) = n-th quintic factorial number divided by 3.

a(n) = n-th quintic factorial number divided by 4.

Zeroless primes that remain prime if any digit is deleted.

Zeroless primes that become nonprime if any digit is deleted.

Nonprime; becomes prime if any digit is deleted (zeros not allowed in the number).

Zeroless nonprimes that remain nonprime if any digit is deleted.

Palindromes P such that Fibonacci iterations starting with (1, P) lead to a "nine digits anagram".

Numbers k such that there are no oblong (promic) palindromes of length k.

Decimal part of a(n)^(1/2) starts with reversal of its integer part: first term of runs.

Decimal part of a(n)^(1/3) starts with reversal of its integer part: first term of runs.

Decimal part of a(n)^(1/4) starts with reversal of its integer part: first term of runs.