-217

Appears in sequences

• Expansion of e.g.f.: sin(sinh(x))*exp(x).at n=7A009492
• arcsinh(sec(x)*sinh(x))=x+3/3!*x^3+5/5!*x^5-217/7!*x^7+2505/9!*x^9...at n=3A012817
• a(n) = 2^n - n^3.at n=9A024013
• a(n) = 8^n-n^6.at n=3A024094
• McKay-Thompson series of class 12E for the Monster group.at n=11A058483
• Generalized sum of divisors function: third diagonal of A060184.at n=44A060186
• Numerators of sequence arising from study of Calabi-Yau manifolds.at n=3A060346
• A measure of how close the golden ratio is to rational numbers.at n=52A066212
• For each n there are uniquely determined numbers a(n) and b(n) and a polynomial p_n(x) such that for all integers m we have Sum_{i=1..m}i^n(i+1)! = a(n)*Sum_{i=1..m} (i+1)! + p_n(m)*(m+2)! + b(n). The sequence b(n) is A074052.at n=7A074051
• Expansion of psi(x^3) / psi(x) in powers of x where psi() is a Ramanujan theta function.at n=29A101195
• G.f. satisfies: A(x) = 1/(1 + x*A(x^8)) and also the continued fraction: 1 + x*A(x^9) = [1; 1/x, 1/x^8, 1/x^64, 1/x^512, ..., 1/x^(8^(n-1)), ...].at n=40A101918
• Matrix inverse of A107719.at n=24A107727
• Expansion of Product_{k>=1} (1 + x^k)^lambda(k) where lambda(k) is the Liouville function, A008836.at n=62A118207
• Expansion of (eta(q) * eta(q^6))^7 / (eta(q^2) * eta(q^3))^5 in powers of q.at n=49A123532
• Expansion of q* (psi(q^9)/phi(q^9))/ (psi(q)/phi(q)) in powers of q where psi(),phi() are Ramanujan theta functions.at n=82A128143
• Expansion of psi(q^3)* phi(-q^3)* chi^2(-q^3)/( psi(-q)* phi(-q^18)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.at n=83A128145
• Numerators of Blandin-Diaz compositional Bernoulli numbers (B^Z^2)_1,n.at n=4A132098
• Row sums of triangle A132898.at n=13A132899
• A triangular sequence of polynomial coefficients of an adjusted root product one polynomial set: w(i,n)=If[i == 1, 1/n!, i]; p(x,n)=n!*Product[x - w[i, n], {i, 0, n}]/x.at n=13A142148
• Coefficients of polynomials based on the generalized factorial at k=2 (A001147): b(n)=b(n-1+k; a(n)=b(n)*a(n-1); p(x,n)=If[n == 0, 1, a(n - 1)*(x - a(n - 1))*Product[x + 1/b(i), {i, 1, n - 1}]].at n=8A144457