-1215

Appears in sequences

• Expansion of e.g.f. sinh(tan(x) + log(x+1)).at n=6A012929
• Expansion of e.g.f. sinh(arctanh(x) + log(x+1)).at n=6A013161
• Inverse Euler transform of {1, primes}.at n=40A030011
• a(0)=1, a(1)=5, a(n) = -3*a(n-1), n>1.at n=6A084244
• Expansion of -x*(1-x)/(1+14*x+x^2)^3.at n=3A122575
• Triangle, T(n, k) = k^6 - n^6 - 5*(n*k)^2*(n^2 - k^2) + 4*n*k*((n*k)^4 - 1), read by rows.at n=11A123964
• a(n) = the numerator of b(n): {b(n)} is such that the continued fraction (of rational terms) [b(1);b(2),...,b(n)] equals the n-th prime, for every positive integer n.at n=32A128270
• Sequence is identical to its third differences in absolute value: a(0), a(1), a(2), a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), with a(0)=a(1)=0, a(2)=1.at n=23A131665
• Triangle T(n, k, m) = t(n,m)/( t(k,m) * t(n-k,m) ) with T(n, 0, m) = T(n, n, m) = 1, where t(n, m) = Product_{j=1..n} Product_{i=1..j-1} ( 1 - (m+1)*(3*i-2) ) and m = 3, read by rows.at n=11A156727
• Triangle T(n, k, m) = t(n,m)/( t(k,m) * t(n-k,m) ) with T(n, 0, m) = T(n, n, m) = 1, where t(n, m) = Product_{j=1..n} Product_{i=1..j-1} ( 1 - (m+1)*(3*i-2) ) and m = 3, read by rows.at n=13A156727
• a(n) = 3^n*A168053(n).at n=5A171557
• Triangle read by rows, e.g.f. exp(x*(z-3/2))*(exp(3*x/2)+2*cos(sqrt(3)*x/2))/3.at n=57A215063
• Triangle read by rows: terms T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k).at n=23A244125
• Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(-1)^n as Sum(k=0..n)T(n,k)*binomial(n,k).at n=33A244140
• Determinant of n X n Hankel matrix whose entries are 1-A010060(i+j), where A010060 is the Thue-Morse sequence.at n=20A274330
• List of nonzero determinants of Unbordered Lights Out matrices UBL_k.at n=1A296353
• Product_{n>=1} (1 + x^n)^a(n) = 1 + x + Sum_{n>=2} prime(n-1) * x^n.at n=40A353161
• Product_{n>=1} (1 + a(n)*x^n) = 1 + x + Sum_{n>=2} prime(n-1)*x^n.at n=40A353606
• Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + x + Sum_{n>=2} prime(n-1)*x^n.at n=40A353951
• Determinant of the matrix [Jacobi(i^2 + 3*i*j + 2*j^2, 2*n + 1)]_{1 < i, j < 2*n}, where Jacobi(a, m) denotes the Jacobi symbol (a / m).at n=4A372314