54096

Appears in sequences

• a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2, a(2)=1, and a(3)=3.at n=13A024741
• Triangle read by rows, defined by T(n,k) = C(n,k)*S2(n,k), 0 <= k <= n, where C(n,k) are the binomial coefficients and S2(n,k) are the Stirling numbers of the second kind.at n=39A090683
• Triangle, read by rows, where the g.f. of row n, R_n(x), is a polynomial of degree n that satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1, with R_0(x) = 1.at n=33A108990
• Third diagonal of triangle A108990, in which the g.f. of row n, R_n(x), satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1.at n=5A108994
• Triangle read by rows: number of nilpotent partial transformations (of an n-element set) of height r (height(alpha) = |Im(alpha)|), 0 <= r < n.at n=30A141618
• Number of horizontal segments in all dispersed Dyck paths of length n (i.e., in all Motzkin paths of length n with no (1,0)-steps at positive heights; a horizontal segment is a maximal sequence of consecutive (1,0)-steps).at n=17A191391
• a(n) = Sum_{i=0..n} digsum_8(i)^4, where digsum_8(i) = A053829(i).at n=31A231683
• a(n) = Sum_{i=0..n} digsum_9(i)^4, where digsum_9(i) = A053830(i).at n=31A231687
• Positive integers n such that the Fibonacci (or Zeckendorf) representation of n^2 is a palindrome.at n=24A288252
• Expansion of Sum_{k>=1} k^3 * x^k/(1 - x^k)^3.at n=31A366135
• Expansion of (1/x) * Series_Reversion( x / ((1+x)^4+x^4) ).at n=6A369126