A384718 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A052750.

1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 49, 0, 1, 4, 21, 128, 729, 0, 1, 5, 32, 243, 2000, 14641, 0, 1, 6, 45, 400, 3993, 41472, 371293, 0, 1, 7, 60, 605, 6912, 85683, 1075648, 11390625, 0, 1, 8, 77, 864, 10985, 153664, 2278125, 33554432, 410338673, 0

Offset

0,8

Links

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

Formula

A(n,k) = k * (2*n+k)^(n-1) for n > 0.

Example

Square array begins:
  1,     1,     1,     1,      1,      1, ...
  0,     1,     2,     3,      4,      5, ...
  0,     5,    12,    21,     32,     45, ...
  0,    49,   128,   243,    400,    605, ...
  0,   729,  2000,  3993,   6912,  10985, ...
  0, 14641, 41472, 85683, 153664, 253125, ...

Prog

(PARI) a(n, k) = if(n==0, 1, k*(2*n+k)^(n-1));

Crossrefs

Columns k=0..2 give A000007, A052750, A097629(n+1).

Cf. A058127, A232006, A384692.

Sequence in context: A384813 A384985 A396994 * A379168 A384721 A384751

Adjacent sequences: A384715 A384716 A384717 * A384719 A384720 A384721

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 08 2025

Status

approved