A370381 Array read by downward antidiagonals: A(n,k) = Sum_{j=0..k+1} binomial(k+2, j+1)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.

1, 1, 3, 1, 7, 13, 1, 15, 45, 71, 1, 31, 145, 319, 461, 1, 63, 453, 1355, 2525, 3447, 1, 127, 1393, 5623, 13241, 22199, 29093, 1, 255, 4245, 23051, 68261, 138219, 215157, 273343, 1, 511, 12865, 93799, 348761, 850031, 1549889, 2282639, 2829325, 1, 1023, 38853, 379835, 1771925, 5193867, 11065437, 18672307, 26340253, 31998903

Offset: 0

Author

Mikhail Kurkov, Feb 17 2024

Keywords

• nonn
• tabl

Examples

			Array begins:
==================================================
n\k|    0     1      2      3       4        5 ...
---+----------------------------------------------
0  |    1     1      1      1       1        1 ...
1  |    3     7     15     31      63      127 ...
2  |   13    45    145    453    1393     4245 ...
3  |   71   319   1355   5623   23051    93799 ...
4  |  461  2525  13241  68261  348761  1771925 ...
5  | 3447 22199 138219 850031 5193867 31604159 ...
  ...
		

Crossrefs

Cf. A003319.

Programs

PARI

A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 1)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-1, k, sum(j=1, k+1, binomial(k+1, j)*v[j])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(5) }

Formula

Conjecture: A(n,0) = A003319(n+2). - Mikhail Kurkov, Oct 27 2024