Sequences

Increasing gaps among twin primes: the largest prime of the starting twin pair.

Increasing gaps among twin primes: the smallest prime of the second twin pair.

Increasing gaps among twin primes: size.

Triangle of flag coefficients [ n k ] (numerators of rational parts).

Triangle of flag coefficients [ n k ] (denominators of rational parts).

The summarize Lucas sequence: summarize the previous two terms, start with 1, 3.

A summarize Fibonacci sequence starting with a(0)=a(1)=0: summarize the previous two terms!.

Expansion of (-1+1/(1-3*x)^3)/(9*x).

Denominator of rational part of Haar measure on Grassmannian space G(n,1).

Expansion of (-1+1/(1-4*x)^4)/(16*x); related to A038846.

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

Erroneous version of A002569.

Triangle of coefficients arising in calculation of A002872 and A002874 (sorting numbers).

Expansion of e.g.f. exp((exp(p*x) - p - 1)/p + exp(x)) for p=4.

The number of partitions of {1..5n} that are invariant under a permutation consisting of n 5-cycles.

Expansion of e.g.f. exp((exp(p*x)-p-1)/p+exp(x)) for p=6.

The number of partitions of {1..7n} that are invariant under a permutation consisting of n 7-cycles.

E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=8.

E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=9.

E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=10.

The number of partitions of {1..(11n)} that are invariant under a permutation consisting of n 11-cycles.

E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=12.

Expansion of (-1+1/(1-5*x)^5)/(25*x); related to A036071.

Expansion of 1/(1-6*x)^6.

Centered cube numbers: (n+1)^7 + n^7.

Centered cube numbers: a(n) = (n+1)^8+n^8.

Centered cube numbers: a(n) = (n+1)^9 + n^9.

Centered cube numbers: (n+1)^10 + n^10.

Centered cube numbers: (n+1)^11 + n^11.

Centered cube numbers: (n+1)^12 + n^12.

Centered cube numbers: (n+1)^13+n^13.

Centered cube numbers: a(n) = (n+1)^14 + n^14.

Centered cube numbers: (n+1)^15 + n^15.

Centered cube numbers: (n+1)^16 + n^16.

Centered cube numbers: a(n) = (n+1)^17 + n^17.

Centered cube numbers: (n+1)^18 + n^18.

Centered cube numbers: (n+1)^19+n^19.

Centered cube numbers: a(n) = (n+1)^20 + n^20.

Centered cube numbers: (n+1)^21 + n^21.

Centered cube numbers: (n+1)^22 + n^22.

Centered cube numbers: (n+1)^23 + n^23.

Centered cube numbers: (n+1)^24 + n^24.

A look-and-say sequence: each term summarizes the previous two terms.

A summarize Fibonacci sequence starting with a(0)=0 and a(1)=2: summarize the previous two terms!.

A summarize Fibonacci sequence starting with a(0)=1 and a(1)=0: summarize the previous two terms!.

A summarize Fibonacci sequence starting with a(0)=1 and a(1)=2: summarize the previous two terms!.

A summarize Fibonacci sequence starting with a(0)=1 and a(1)=4: summarize the previous two terms!.

A summarize Fibonacci sequence starting with a(0)=2 and a(1)=0: summarize the previous two terms!.

A summarize Fibonacci sequence starting with a(0)=2 and a(1)=1: summarize the previous two terms!.

A summarize Fibonacci sequence starting with a(0)=2 and a(1)=2: summarize the previous two terms!.