22584

Appears in sequences

• a(1)=1, a(n) is the smallest integer > a(n-1) such that the sum of elements of the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals n*(n+1)/2 the n-th triangular number.at n=26A071184
• Starting positions of strings of three 5's in the decimal expansion of Pi.at n=21A083620
• Array read by antidiagonals: T(m,n) = Sum_{i=1..m} i*(n-1+i)!.at n=24A100630
• Table read by antidiagonals: T(m,n) gives the ordinal number in the table of permutations of length n+1 of the permutation which reverses the first m+1 items on a list of length n+1, leaving the remaining items unaltered. For example, T(5,7) is 28494 and the 28494th row of the permutation table of order 8 is 5 4 3 2 1 0 6 7.at n=44A100711
• Expansion of q / (chi(-q) * chi(-q^11))^2 in powers of q where chi() is a Ramanujan theta function.at n=31A123631
• Values of y in solutions (x,y,z) to the Diophantine equation x^3-x^2+y^3-y^2=z^3-z^2, with 1<x<y<z arranged in order of increasing x.at n=33A138668
• G.f. satisfies: A(x) = exp( Sum_{n>=1} (2^n + A(x))^n * x^n/n ).at n=4A163138
• Number of line segments connecting exactly 7 points in an n X n grid of points.at n=39A177723
• Number of nX2 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.at n=12A201066
• The Szeged index of a benzenoid consisting of a linear chain of n hexagons.at n=10A245830
• Least integer m > 0 with pi(m*n) = sigma(m) + sigma(n), where pi(.) and sigma(.) are given by A000720 and A000203 respectively.at n=26A247673
• Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(k+1).at n=10A261451
• Expansion of (Sum_{k>=0} x^(k^2*(k+1)^2/4))^12.at n=47A284641
• Number of odd semiprimes between 2^(n-1) and 2^n.at n=18A362318
• Number of alpha-labelings of trees on n vertices.at n=11A392797