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

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

Example

   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, ...

Prog

(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

Crossrefs

Cf. A152011.

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

Sequence in context: A110545 A104798 A243238 * A231731 A143358 A143729

Adjacent sequences: A169626 A169627 A169628 * A169630 A169631 A169632

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 03 2010

Status

approved