A169629 Array T(n,k) read by antidiagonals: T(n,k) = Sum_{v=1..n, v odd} binomial(n,v)*k^v.

1, 2, 2, 4, 4, 3, 8, 14, 6, 4, 16, 40, 36, 8, 5, 32, 122, 120, 76, 10, 6, 64, 364, 528, 272, 140, 12, 7, 128, 1094, 2016, 1684, 520, 234, 14, 8, 256, 3280, 8256, 7448, 4400, 888, 364, 16, 9, 512, 9842, 32640, 40156, 21280, 9966, 1400, 536, 18, 10

Offset: 1

Author

Roger L. Bagula, Mar 03 2010

Keywords

• nonn
• tabl

Comments

Antidiagonal sums are: 1, 4, 11, 32, 105, 366, 1387, ...

Examples

			   1,    2,    3,     4,      5,      6,       7, ...
   2,    4,    6,     8,     10,     12,      14, ...
   4,   14,   36,    76,    140,    234,     364, ...
   8,   40,  120,   272,    520,    888,    1400, ...
  16,  122,  528,  1684,   4400,   9966,   20272, ...
  32,  364, 2016,  7448,  21280,  51012,  107744, ...
  64, 1094, 8256, 40156, 148160, 450834, 1188544, ...
		

Crossrefs

Cf. A152011.

Cf. A005843 (2nd line), A079908 (3rd line), A105374 (4th line).

Programs

PARI

tabl(nn) = {for (n=1, nn, for (k=1, nn, print1(sum(v=1, n, (v%2)*binomial(n, v)*k^v), ", ");); print(););} \\ Michel Marcus, Jul 22 2015