19524

Appears in sequences

• Scaled sums of odd reciprocals: a(n) = (2*n + 1)!!*(Sum_{k=0..n} 1/(2*k + 1)).at n=5A004041
• Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of x.at n=22A028338
• a(n)=Sum{T(n,j): j=1,2,...,n}, array T given by A048201.at n=29A048209
• Generalized Stirling number triangle of first kind.at n=16A051338
• Second unsigned column of triangle A051338.at n=5A051524
• Triangle read by rows: for 0 <= k < n, a(n, k) is the sum of the products of all subsets of {n-k, n-k+1, ..., n} with k members.at n=49A093905
• a(n) = n!*[x^n] (log(x+1) * Sum_{j=0..n} C(2*n,j)*x^j).at n=4A098118
• a(n) = (Sum 1/k) (Product k), where both the sum and product are over those k where 1 <= k <= n/2 and gcd(k,n) = 1.at n=24A099001
• Triangle of coefficients in expansion of (1+x)*(1+3x)*(1+5x)*(1+7x)*...*(1+(2n-1)x).at n=26A109692
• a(1)=1. a(n+1) = sum{k=1 to n} (a(k)th integer from among those positive integers which are coprime to a(n+1-k)).at n=14A132275
• Square array, read by antidiagonals, where row n+1 is generated from row n by first removing terms at positions [(m+2)^2/4 - 1] for m>=0 and then taking partial sums, starting with all 1's in row 0.at n=39A135876
• Fifth right hand column of triangle A165674.at n=5A165677
• G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..n} (1 + k*x)^2.at n=6A208829
• Number of ordered triples (w,x,y) with all terms in {-n, ..., -1, 1, ..., n} and 4w + x + y > 0.at n=17A211629
• Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y|,|y-w| distinct.at n=30A213493
• Principal diagonal of the convolution array A213505.at n=7A213546
• Number of n X 3 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.at n=29A223833
• Triangle read by rows, k!*s_2(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0.at n=22A225475
• Triangle T(n, k) read by rows giving number of non-equivalent ways to choose k points in an equilateral triangle grid of side n.at n=47A231655
• Triangle T(n, k) read by rows giving number of non-equivalent ways to choose k points in an equilateral triangle grid of side n.at n=54A231655