A188481 Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/(2*sqrt(1-4x))).

1, 4, 1, 16, 7, 1, 64, 38, 10, 1, 256, 187, 69, 13, 1, 1024, 874, 406, 109, 16, 1, 4096, 3958, 2186, 748, 158, 19, 1, 16384, 17548, 11124, 4570, 1240, 216, 22, 1, 65536, 76627, 54445, 25879, 8485, 1909, 283, 25, 1, 262144, 330818, 259006, 138917, 52984, 14471, 2782, 359, 28, 1

Offset

0,2

Comments

Row sums = A141223;

Diagonal sums = A188482;

Inverse matrix: (1/(1+2x)^2, x(1+x)/(1+2x)^2).

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = [x^n] ((1-sqrt(1-4*x))/(2*sqrt(1-4*x)))^k/(1-4*x).

Recurrence: T(n+1,k+1) = T(n,k) + 3*T(n,k-1) + T(n,k-2) - T(n,k-3) + T(n,k-4) - T(n,k-5) + ...

Example

Triangle begins:
      1;
      4,     1;
     16,     7,     1;
     64,    38,    10,     1;
    256,   187,    69,    13,    1;
   1024,   874,   406,   109,   16,    1;
   4096,  3958,  2186,   748,  158,   19,   1;
  16384, 17548, 11124,  4570, 1240,  216,  22,  1;
  65536, 76627, 54445, 25879, 8485, 1909, 283, 25, 1;

Mathematica

Flatten[Table[Sum[Binomial[n+i, n]Binomial[n-i, k]2^(n-k-i), {i, 0, n-k}], {n, 0, 8}, {k, 0, 8}]]

Prog

(Maxima) create_list(sum(binomial(n+i, n)*binomial(n-i, k)*2^(n-k-i), i, 0, n-k), n, 0, 8, k, 0, n);

Crossrefs

Cf. A141223, A188482.

Sequence in context: A285281 A285267 A067425 * A138681 A038231 A104855

Adjacent sequences: A188478 A188479 A188480 * A188482 A188483 A188484

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, Apr 01 2011

Extensions

Comment corrected by Philippe Deléham, Jan 22 2014

Status

approved