A038304 Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*2^j.

1, 10, 2, 100, 40, 4, 1000, 600, 120, 8, 10000, 8000, 2400, 320, 16, 100000, 100000, 40000, 8000, 800, 32, 1000000, 1200000, 600000, 160000, 24000, 1920, 64, 10000000, 14000000, 8400000, 2800000, 560000, 67200, 4480, 128, 100000000

Offset

0,2

Links

Table of n, a(n) for n=0..36.

B. N. Cyvin, J. Brunvoll, and S. J. Cyvin, Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), 109-121.

Formula

G.f.: 1/(1 - 10*x - 2*x*y). - Stefano Spezia, Apr 28 2024

Example

From Stefano Spezia, Apr 28 2024: (Start)
Triangle begins:
       1;
      10,      2;
     100,     40,     4;
    1000,    600,   120,    8;
   10000,   8000,  2400,  320,  16;
  100000, 100000, 40000, 8000, 800, 32;
  ...
(End)

Mathematica

Table[Binomial[i, j]*10^(i-j)*2^j, {i, 0, 7}, {j, 0, i}]//Flatten (* Stefano Spezia, Apr 28 2024 *)

Crossrefs

Cf. A000079 (right diagonal), A001021 (row sums), A011557 (1st column).

Sequence in context: A054841 A185076 A178643 * A290308 A354941 A352689

Adjacent sequences: A038301 A038302 A038303 * A038305 A038306 A038307

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane

Status

approved