A379587 Array read by ascending antidiagonals: A(n, k) = (k^n - 1)^2/(k - 1), with k >= 2.

0, 1, 0, 9, 2, 0, 49, 32, 3, 0, 225, 338, 75, 4, 0, 961, 3200, 1323, 144, 5, 0, 3969, 29282, 21675, 3844, 245, 6, 0, 16129, 264992, 348843, 97344, 9245, 384, 7, 0, 65025, 2389298, 5589675, 2439844, 335405, 19494, 567, 8, 0, 261121, 21516800, 89467563, 61027344, 12090125, 960000, 37303, 800, 9, 0

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Formula

G.f. of column k: (1 - k)*x*(1 + k*x)/((1 - x)*(1 - k*x)*(1 - k^2*x)).

E.g.f. of column k: exp(x)*(1 - 2*exp((k-1)*x) + exp((k^2-1)*x))/(k - 1).

A(2, n) = A027620(n-2) for n > 1.

Example

The array begins as:
    0,     0,      0,       0,        0,        0, ...
    1,     2,      3,       4,        5,        6, ...
    9,    32,     75,     144,      245,      384, ...
   49,   338,   1323,    3844,     9245,    19494, ...
  225,  3200,  21675,   97344,   335405,   960000, ...
  961, 29282, 348843, 2439844, 12090125, 47073606, ...
  ...

Mathematica

A[n_, k_]:=(k^n-1)^2/(k-1); Table[A[n-k+2, k], {n, 0, 9}, {k, 2, n+2}]//Flatten

Crossrefs

Cf. A027620, A060867 (k=2), A060868 (k=3), A060869 (k=4), A060870 (k=5), A060871 (k=7), A361475, A379588 (antidiagonal sums).

Sequence in context: A388559 A240985 A296460 * A387170 A319533 A010160

Adjacent sequences: A379584 A379585 A379586 * A379588 A379589 A379590

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Dec 26 2024

Status

approved