-454

Appears in sequences

• cos(tanh(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+13/4!*x^4-20/5!*x^5...at n=6A013122
• Binomial transform of pentanacci numbers A074048: a(n)=Sum((-1)^k*Binomial(n,k)*A074048(k),(k=0,..,n)).at n=10A075194
• Alternating row sums of triangle A090447.at n=5A090451
• Triangle read by rows: numerators of Cotesian numbers C(n,k) (0 <= k <= n).at n=40A100640
• Triangle of coefficients of (1 - x)^n*B_n(x/(1 - x)), where B_n(x) is the n-th Bell polynomial.at n=41A122753
• Expansion of chi(-q) * chi(-q^15) / (chi(-q^6) * chi(-q^10)) in powers of q where chi() is a Ramanujan theta function.at n=47A132968
• Expansion of psi(-q^3) / f(q) where psi(), f() are Ramanujan theta functions.at n=17A139135
• Expansion of (phi(q) / phi(q^3) - 1) / 2 in powers of q where phi() is a Ramanujan theta function.at n=51A139139
• Row sums of the swinging derangement triangle (A163770).at n=6A163773
• A symmetrical triangle:t(n,m)=Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1.at n=16A176565
• A symmetrical triangle:t(n,m)=Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1.at n=19A176565
• Expansion of the unique normalized cusp form of Gamma_0(5) of weight 6 in powers of q.at n=17A226347
• Unreduced numerators in triangle that leads to the Euler numbers A198631(n)/A006519(n+1).at n=35A238800
• Expansion of Product_{k>=1} (1 - x^k)^q(k), where q(k) = number of partitions of k into distinct parts (A000009).at n=37A304783
• a(n) = Sum_{d|n} mu(d) * binomial(d + n/d - 2, d-1).at n=51A338656
• a(n) = Sum_{k=0..n} (-1)^k * binomial(4*k,n-k) * Catalan(k).at n=8A360085