A187926 Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/2).

1, 4, 1, 16, 5, 1, 64, 22, 6, 1, 256, 93, 29, 7, 1, 1024, 386, 130, 37, 8, 1, 4096, 1586, 562, 176, 46, 9, 1, 16384, 6476, 2380, 794, 232, 56, 10, 1, 65536, 26333, 9949, 3473, 1093, 299, 67, 11, 1, 262144, 106762, 41226, 14893, 4944, 1471, 378, 79, 12, 1, 1048576, 431910, 169766, 63004, 21778, 6885, 1941, 470, 92, 13, 1

Offset: 0

Author

Emanuele Munarini, Mar 16 2011

Keywords

• nonn
• tabl
• easy

Comments

Row sums are A000346.

Examples

			Triangle begins:
1,
4,1,
16,5,1,
64,22,6,1,
256,93,29,7,1,
1024,386,130,37,8,1,
4096,1586,562,176,46,9,1,
16384,6476,2380,794,232,56,10,1,
65536,26333,9949,3473,1093,299,67,11,1
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5150

Crossrefs

Cf. A000346

Programs

Mathematica

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

Maxima

create_list(sum(binomial(n+i,n)*2^(n-k-i),i,0,n-k),n,0,10,k,0,n);

Formula

a(n,k) = sum(binomial(n+i,n)*2^(n-k-i),i=0..n-k)

Recurrence: a(n+1,k+1) = a(n,k) + a(n,k+1) + a(n,k+2) + ... + a(n,n).