A136501 Triangle, read by rows, where T(n,k) = C(2^k,n-k) for n>=k>=0.

1, 1, 1, 0, 2, 1, 0, 1, 4, 1, 0, 0, 6, 8, 1, 0, 0, 4, 28, 16, 1, 0, 0, 1, 56, 120, 32, 1, 0, 0, 0, 70, 560, 496, 64, 1, 0, 0, 0, 56, 1820, 4960, 2016, 128, 1, 0, 0, 0, 28, 4368, 35960, 41664, 8128, 256, 1, 0, 0, 0, 8, 8008, 201376, 635376, 341376, 32640, 512, 1, 0, 0, 0, 1, 11440, 906192, 7624512, 10668000, 2763520, 130816, 1024, 1

Offset

0,5

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Example

Triangle begins:
  1;
  1, 1;
  0, 2, 1;
  0, 1, 4,  1;
  0, 0, 6,  8,     1;
  0, 0, 4, 28,    16,      1;
  0, 0, 1, 56,   120,     32,       1;
  0, 0, 0, 70,   560,    496,      64,        1;
  0, 0, 0, 56,  1820,   4960,    2016,      128,       1;
  0, 0, 0, 28,  4368,  35960,   41664,     8128,     256,      1;
  0, 0, 0,  8,  8008, 201376,  635376,   341376,   32640,    512,    1;
  0, 0, 0,  1, 11440, 906192, 7624512, 10668000, 2763520, 130816, 1024, 1;

Mathematica

Table[Binomial[2^k, n-k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 15 2021 *)

Prog

(PARI) T(n, k)=binomial(2^k, n-k)
(Magma) [Binomial(2^k, n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 15 2021
(Sage) flatten([[binomial(2^k, n-k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 15 2021

Crossrefs

Cf. A014070 (central terms), A121688 (row sums), A136502 (matrix inverse).

Sequence in context: A366834 A109970 A116088 * A180983 A127709 A343730

Adjacent sequences: A136498 A136499 A136500 * A136502 A136503 A136504

Keyword

nonn,tabl

Author

Paul D. Hanna, Jan 01 2008

Status

approved