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URL: https://oeis.org/A373967

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A373967
Triangle read by rows: T(n,k) = (-1)^n * n! + (-1)^(k+1) * k! for n >= 2 and 1 <= k <= n-1.
1
3, -5, -8, 25, 22, 30, -119, -122, -114, -144, 721, 718, 726, 696, 840, -5039, -5042, -5034, -5064, -4920, -5760, 40321, 40318, 40326, 40296, 40440, 39600, 45360, -362879, -362882, -362874, -362904, -362760, -363600, -357840, -403200, 3628801, 3628798, 3628806, 3628776, 3628920, 3628080, 3633840, 3588480, 3991680
OFFSET
2,1
FORMULA
Integral_{1..e} (log(x)^k - log(x)^n) dx = A373966(n,k)*e + T(n,k).
EXAMPLE
Triangle begins:
3;
-5, -8;
25, 22, 30;
-119, -122, -114, -144;
721, 718, 726, 696, 840;
-5039, -5042, -5034, -5064, -4920, -5760;
...
MATHEMATICA
T[n_, k_]:= (-1)^n*n! + (-1)^(k+1)*k!; Table[T[n, k], {n, 2, 10}, {k, n-1}]// Flatten (* Stefano Spezia, Jun 24 2024 *)
CROSSREFS
Unsigned diagonals: A001048, A213167.
Sequence in context: A108460 A249951 A368740 * A353605 A027520 A195548
KEYWORD
sign,tabl,easy
AUTHOR
Mohammed Yaseen, Jun 24 2024
STATUS
approved