Triangle read by rows. The Faulhaber numbers. F(0, k) = 1 and otherwise F(n, k) = (n + 1)!*(-1)^(k+1)*Sum_{j=0..floor((k-1)/2)} C(2*k-2*j, k+1)*C(2*n+1, 2*j+1) * Bernoulli(2*n-2*j) / (k - j).
A354042
Triangle read by rows. The Faulhaber numbers. F(0, k) = 1 and otherwise F(n, k) = (n + 1)!*(-1)^(k+1)*Sum_{j=0..floor((k-1)/2)} C(2*k-2*j, k+1)*C(2*n+1, 2*j+1) * Bernoulli(2*n-2*j) / (k - j).
Terms
- a(0) =1a(1) =0a(2) =1a(3) =0a(4) =-1a(5) =2a(6) =0a(7) =4a(8) =-8a(9) =6a(10) =0a(11) =-36a(12) =72a(13) =-60a(14) =24a(15) =0a(16) =600a(17) =-1200a(18) =1020a(19) =-480a(20) =120a(21) =0a(22) =-16584a(23) =33168a(24) =-28320a(25) =13776a(26) =-4200a(27) =720a(28) =0a(29) =705600
External references
- oeis: A354042