-10240

Appears in sequences

• Triangle T, read by rows, where matrix power T^2 has powers of 2 in the secondary diagonal: [T^2](n+1,n) = 2^(n+1), with all 1's in the main diagonal and zeros elsewhere.at n=23A117250
• Triangle T(n,k) = k*A053120(n,k).at n=52A136160
• Denominators of a BBP series for Pi/4.at n=9A164916
• Expansion of x * (1 - 2*x + 8*x^5 - 8*x^6) / (1 - 4*x^4)^2.at n=23A235789
• Triangle read by rows: T(0,0) = 1; T(n,k) = 2*T(n-1,k) - 2*T(n-2,k-1) + T(n-3,k-2) for k = 0..floor(2*n/3); T(n,k)=0 for n or k < 0.at n=45A304213
• Consider the e.g.f. C(x,y) = sqrt(1/2) * Sum_{n>=0} Sum_{k=0..2*n} T(n,k) * x^(2*n-k) * y^k / ((2*n-k)!*k!) and related functions S(x,y) and D(x,y), as defined in the Formula section. Sequence gives the triangular array of coefficients T(n,k) (n>=0, 0<=k<=2*n) of C(x,y).at n=53A326801
• Consider the e.g.f. C(x,y) = sqrt(1/2) * Sum_{n>=0} Sum_{k=0..2*n} T(n,k) * x^(2*n-k) * y^k / ((2*n-k)!*k!) and related functions S(x,y) and D(x,y), as defined in the Formula section. Sequence gives the triangular array of coefficients T(n,k) (n>=0, 0<=k<=2*n) of C(x,y).at n=58A326801
• Consider the e.g.f. D(x,y) = sqrt(1/2) * Sum_{n>=0} Sum_{k=0..2*n} T(n,k) * x^(2*n-k) * y^k / ((2*n-k)!*k!) and related functions S(x,y) and C(x,y), as defined in the Formula section. Sequence gives the triangular array of coefficients T(n,k) (n>=0, 0<=k<=2*n) of D(x,y).at n=53A326802
• a(0) = 0, a(1) = 1, for n > 1, a(n) = 2^(n+1) - 3*(sigma((2^n)-1) - sigma((2^(n-1))-1)).at n=14A329892
• G.f. A(x) satisfies A(x) = ( 1 + 16*x*(1 + A(x)) )^(1/4).at n=4A371988