OFFSET
0,2
COMMENTS
Row sums are A000346.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5150
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).
EXAMPLE
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
MATHEMATICA
Table[Sum[Binomial[n + i, n]2^(n - k - i), {i, 0, n - k}], {n, 0, 8}, {k, 0, 8}]//MatrixForm
PROG
(Maxima) create_list(sum(binomial(n+i, n)*2^(n-k-i), i, 0, n-k), n, 0, 10, k, 0, n);
CROSSREFS
KEYWORD
AUTHOR
Emanuele Munarini, Mar 16 2011
STATUS
approved