A363779 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} x^(j^3))^k.

1, 1, 0, 1, -1, 0, 1, -2, 1, 0, 1, -3, 3, -1, 0, 1, -4, 6, -4, 1, 0, 1, -5, 10, -10, 5, -1, 0, 1, -6, 15, -20, 15, -6, 1, 0, 1, -7, 21, -35, 35, -21, 7, -1, 0, 1, -8, 28, -56, 70, -56, 28, -8, 0, 0, 1, -9, 36, -84, 126, -126, 84, -36, 7, 1, 0, 1, -10, 45, -120, 210, -252, 210, -120, 42, -4, -2, 0

Offset

0,8

Links

Table of n, a(n) for n=0..77.

Formula

T(0,k) = 1; T(n,k) = -(k/n) * Sum_{j=1..n} A363783(j) * T(n-j,k).

Example

Square array begins:
  1,  1,  1,   1,   1,    1,    1, ...
  0, -1, -2,  -3,  -4,   -5,   -6, ...
  0,  1,  3,   6,  10,   15,   21, ...
  0, -1, -4, -10, -20,  -35,  -56, ...
  0,  1,  5,  15,  35,   70,  126, ...
  0, -1, -6, -21, -56, -126, -252, ...
  0,  1,  7,  28,  84,  210,  462, ...

Crossrefs

Columns k=0..3 give A000007, A323633, A363776, A363777.

Main diagonal gives A363781.

Cf. A290054, A363778, A363783.

Sequence in context: A213888 A119337 A213889 * A373164 A110555 A097805

Adjacent sequences: A363776 A363777 A363778 * A363780 A363781 A363782

Keyword

sign,tabl

Author

Seiichi Manyama, Jun 21 2023

Status

approved