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A169629
Array T(n,k) read by antidiagonals: T(n,k) = Sum_{v=1..n, v odd} binomial(n,v)*k^v.
0
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, ...
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
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 03 2010
STATUS
approved