-546

Appears in sequences

• Expansion of Product_{m >= 1} (1-m*q^m)^13.at n=4A022673
• Expansion of Product_{m>=1} (1+m*q^m)^-18.at n=3A022710
• McKay-Thompson series of class 30G for the Monster group.at n=43A058618
• a(n) = (-1)^n*(2*n - 1)*CatalanNumber(n - 2) for n >= 2, a(n) = n for n = 0, 1.at n=7A078718
• Binomial transform of (1,-1,4,-16,64,-256,1024,...) = (3*0^n-(-4)^n)/4.at n=7A084567
• Inverse binomial transform of number triangle A105632.at n=60A105847
• Riordan array ((1-x)/(1+x), x/(1+x)^2).at n=51A110162
• Riordan array (1/(1+x), x*(1-2*x)/(1+x)^2).at n=30A110522
• Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p[n,x] defined by p[ -1,x]=0, p[0,x]=1, p[1,x]=-x, p[n,x]=x*p[n-1,x]-(n-1)*p[n- 2,x]+(n-2)*p[n-3,x] for n>=2 (0<=k<=n).at n=61A123730
• Riordan array ((1+3*x-sqrt(1+2*x+9*x^2))/(2*x),(1+3*x-sqrt(1+2*x+9*x^2))/2).at n=47A125694
• Scaled coefficient table for Chebyshev polynomials 2*T(2*n, sqrt(x)/2) (increasing even scaled powers, without zero entries).at n=51A127677
• Expansion of q^(-1) * chi(-q)^2 * chi(-q^15)^2 / (chi(-q^3) * chi(-q^5)) in powers of q where chi() is a Ramanujan theta function.at n=43A133098
• McKay-Thompson series of class 30G for the Monster group with a(0) = -1.at n=43A135213
• Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial h(n,x) with h(0,x)=1, h(1,x)=1-x and recursively h(n,x) = 1 + n -(1-x)*(1-h(n-1,x)) - n*h(n-2,x).at n=39A136247
• Expansion of f(-q^6) * f(-q^10) / (f(q) * f(q^15)) in powers of q where f() is a Ramanujan theta function.at n=21A145728
• Triangle read by rows, characteristic polynomials of Cartan ring matrices.at n=48A152060
• Triangle: q=2; m=1; t(n,k) = If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m) = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].at n=31A156593
• Triangle: q=2; m=1; t(n,k) = If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m) = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].at n=32A156593
• Irregular triangle with the terms in the Staudt-Clausen theorem for the nonzero Bernoulli numbers multiplied by the product of the associated primes.at n=25A165908
• Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial sum_{k=0..infinity} (2*k+1)^n*binomial(x,k) / 2^x.at n=48A176668