111465

Appears in sequences

• Denominators of continued fraction convergents to sqrt(865).at n=13A042671
• Numbers k such that k and k^2 use only the digits 1, 2, 4, 5 and 6.at n=63A136988
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k increasing odd cycles (0<=k<=n). A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . A cycle is said to be odd if it has an odd number of entries. For example, the permutation (152)(347)(6)(8) has 3 increasing odd cycles.at n=45A186761
• Number of permutations of {1,2,...,n} having no increasing odd cycles. A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . A cycle is said to be odd if it has an odd number of entries.at n=9A186762
• E.g.f.: exp( Sum_{n>=1} x^(2*n) / (2*n*(2*n-1)) ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.at n=5A211393
• a(n) = Sum_{k=0..n} binomial(3*n+2,k) * binomial(3*n-k-1,n-k).at n=5A386836