A365372 Array read by ascending antidiagonals: A(n, k) = n*(k*n^2 - 1) with k > 0.

0, 6, 1, 24, 14, 2, 60, 51, 22, 3, 120, 124, 78, 30, 4, 210, 245, 188, 105, 38, 5, 336, 426, 370, 252, 132, 46, 6, 504, 679, 642, 495, 316, 159, 54, 7, 720, 1016, 1022, 858, 620, 380, 186, 62, 8, 990, 1449, 1528, 1365, 1074, 745, 444, 213, 70, 9, 1320, 1990, 2178, 2040, 1708, 1290, 870, 508, 240, 78, 10

Offset

1,2

Links

Table of n, a(n) for n=1..66.

Formula

G.f.: x*y*(x^2*y + y - 2*x*(y - 3))/((1 - x)^4*(1 - y)^2).

1st column: A(n, 1) = A007531(n+1).

2nd row: A(2, n) = A017137(n-1).

Example

The array begins:
    0,   1,   2,   3,    4,    5, ...
    6,  14,  22,  30,   38,   46, ...
   24,  51,  78, 105,  132,  159, ...
   60, 124, 188, 252,  316,  380, ...
  120, 245, 370, 495,  620,  745, ...
  210, 426, 642, 858, 1074, 1290, ...
  ...

Mathematica

A[n_, k_]:=n(k n^2-1); Table[A[n-k+1, k], {n, 11}, {k, n}]//Flatten

Crossrefs

Cf. A007531, A017137, A035328 (k=4), A058895 (main diagonal), A365373 (antidiagonal sums).

Sequence in context: A185678 A286893 A118394 * A278906 A281517 A338865

Adjacent sequences: A365369 A365370 A365371 * A365373 A365374 A365375

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Sep 02 2023

Status

approved