A013628 Triangle of coefficients in expansion of (4 + 5*x)^n.

1, 4, 5, 16, 40, 25, 64, 240, 300, 125, 256, 1280, 2400, 2000, 625, 1024, 6400, 16000, 20000, 12500, 3125, 4096, 30720, 96000, 160000, 150000, 75000, 15625, 16384, 143360, 537600, 1120000, 1400000, 1050000, 437500, 78125, 65536, 655360, 2867200, 7168000, 11200000, 11200000, 7000000, 2500000, 390625

Offset

0,2

Links

Table of n, a(n) for n=0..44.

Formula

G.f.: 1/(1 - x*(4 + 5*y)).

Example

Triangle begins as:
    1;
    4,    5;
   16,   40,   25;
   64,  240,  300,  125;
  256, 1280, 2400, 2000, 625;
  ...

Mathematica

row[n_]:=CoefficientList[Series[(4+5x)^n, {x, 0, n}], x]; Array[row, 9, 0]//Flatten (* Stefano Spezia, Jun 29 2025 *)

Crossrefs

Cf. A000302 (1st column), A000351 (diagonal), A001019 (row sums).

Sequence in context: A284869 A057729 A110278 * A394978 A127007 A007837

Adjacent sequences: A013625 A013626 A013627 * A013629 A013630 A013631

Keyword

tabl,nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Stefano Spezia, Jun 29 2025

Status

approved