12593

Properties

Appears in sequences

• Expansion of e.g.f.: exp(sinh(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-33/5!*x^5...at n=8A013488
• Expansion of Product_{m>=1} (1+m*q^m)^-28.at n=4A022720
• a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (1, p(1), p(2), ...), t = (F(2), F(3), ...).at n=15A024481
• a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (1, p(1), p(2), ...), t = (F(2), F(3), F(4), ...).at n=14A025101
• Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026907.at n=12A026918
• Numbers whose set of base-16 digits is {1,3}.at n=24A032923
• a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), a(n)/11 if 11|a(n), a(n)/13 if 13|a(n), otherwise 17*a(n)+1.at n=25A057534
• Numbers n whose sum of divisors and number of divisors are both triangular numbers.at n=35A070996
• a(n) = (-1)^n*b(2n-1,2) where b(n,p) = Sum_{k=0..n} p^k*C(2*k,k)*C(n+k,n-k)*B(k) and B(k) = k-th Bernoulli number.at n=3A095363
• Row sums of triangle A115237.at n=26A115238
• Difference between squares of legs of primitive Pythagorean triangles, sorted (with multiplicity).at n=31A127923
• Positive numbers of the form x^4 - 6 * x^2 * y^2 + y^4 (where x,y are integers).at n=31A135789
• 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=36A186761
• 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=8A186762
• Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.at n=37A214375
• Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.at n=2A234116
• Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.at n=1A234117
• T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.at n=7A234122
• T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.at n=8A234122
• Number of partitions p of n such that median(p) = multiplicity(min(p)).at n=49A240214