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

2,2

Links

Table of n, a(n) for n=2..46.

Formula

Integral_{1..e} (log(x)^k - log(x)^n) dx = T(n,k)*e + A373967(n,k).

Example

Triangle begins:
    -1;
     2,    3;
    -9,   -8,  -11;
    44,   45,   42,   53;
  -265, -264, -267, -256, -309;
  1854, 1855, 1852, 1863, 1810, 2119;
  ...

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 *)

Crossrefs

Cf. A153805, A373967.

Unsigned columns: A000166, A000240.

Unsigned diagonals: A000255, A018934.

Sequence in context: A378330 A086565 A008291 * A261525 A122665 A133066

Adjacent sequences: A373963 A373964 A373965 * A373967 A373968 A373969

Keyword

sign,tabl,easy

Author

Mohammed Yaseen, Jun 24 2024

Status

approved