A373966 Triangle read by rows: T(n,k) = (-1)^(n+1) * A000166(n) + (-1)^(k) * A000166(k) for n >= 2 and 1 <= k <= n-1.
-1, 2, 3, -9, -8, -11, 44, 45, 42, 53, -265, -264, -267, -256, -309, 1854, 1855, 1852, 1863, 1810, 2119, -14833, -14832, -14835, -14824, -14877, -14568, -16687, 133496, 133497, 133494, 133505, 133452, 133761, 131642, 148329, -1334961, -1334960, -1334963, -1334952, -1335005, -1334696, -1336815, -1320128, -1468457
Offset: 2
Examples
Triangle begins:
-1;
2, 3;
-9, -8, -11;
44, 45, 42, 53;
-265, -264, -267, -256, -309;
1854, 1855, 1852, 1863, 1810, 2119;
...
Crossrefs
Programs
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Mathematica
T[n_,k_]:= (-1)^(n+1)*Subfactorial[n] + (-1)^k*Subfactorial[k]; Table[T[n,k],{n,2,10},{k,n-1}]// Flatten (* Stefano Spezia, Jun 24 2024 *)
Formula
Integral_{1..e} (log(x)^k - log(x)^n) dx = T(n,k)*e + A373967(n,k).