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

Author

Paul D. Hanna, Jan 01 2008

Keywords

• nonn
• tabl

Examples

			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;
		

Links

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

Crossrefs

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

Programs

Magma

[Binomial(2^k, n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 15 2021

Mathematica

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

PARI

T(n,k)=binomial(2^k,n-k)

Sage

flatten([[binomial(2^k, n-k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 15 2021