37632

Appears in sequences

• Glaisher's function V(n).at n=48A002611
• Expansion of e.g.f.: arctan(sech(x)*log(x+1))=x-1/2!*x^2-3/3!*x^3+12/4!*x^4+43/5!*x^5...at n=8A012873
• a(n) = n^3 * Product_{p|n, p prime} (1 + 1/p).at n=27A033196
• Triangle T(n,k), n >= 2, n+1 <= k <= 2*n-1, number of permutations p of 1,...,n, with max(p(i)+p(i-1), i=2..n) = k.at n=31A064484
• Coefficients in expansion of Eisenstein series -q*E'_2.at n=27A076835
• Sum of three solutions of the Diophantine equation x^2 - y^2 = z^3.at n=16A085409
• Triangle T(n,k), 0<=k<=n, read by rows, defined by Sum_{k = 0..n} T(n,k)*x^k = Sum_{k = 0..n} binomial(n,k)*(x+k)^n.at n=33A095677
• Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).at n=7A100313
• Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k peaks (1 <= k <= n).at n=39A114656
• Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k double rises (0 <= k <= n-1).at n=41A114687
• a(n) = (n^3 - n^2)*2^n.at n=6A128985
• a(n) = -(u^n-1)*(v^n-1) with u = 2+sqrt(3), v = 2-sqrt(3).at n=7A129743
• Number of permutations of floor(i*7/3), i=0..n-1, with all sums of 6 adjacent terms unique.at n=7A152377
• Number of permutations of floor(i*7/5), i=0..n-1, with all sums of 6 adjacent terms unique.at n=7A152379
• Number of subsets S of {1,2,3,...,n} with the property that if x is a member of S then at least one of x/2 and 2x is also a member of S.at n=32A172148
• Number of subsets S of {1,2,3,...,n} with the property that if x is a member of S then at least one of x/2 and 2x is also a member of S.at n=31A172148
• Triangle read by rows: T(n,k) = binomial(n,k)*(binomial(n-1,k-1)*binomial(n+1,k+1) + binomial(n-1,k)*binomial(n+1,k)), with T(0,0) = 1.at n=38A174148
• Triangle read by rows: T(n,k) = binomial(n,k)*(binomial(n-1,k-1)*binomial(n+1,k+1) + binomial(n-1,k)*binomial(n+1,k)), with T(0,0) = 1.at n=42A174148
• Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A003500(n)) ), where A003500(n) = (2+sqrt(3))^n + (2-sqrt(3))^n.at n=15A174500
• Expansion of l.g.f. Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^4 *x^k ] *x^n/n.at n=5A181069