A371567 Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + (k+1)*Sum_{j=0..k} A(n-1,j) with A(0,k) = k+1, n >= 0, k >= 0.

1, 2, 3, 3, 9, 12, 4, 22, 46, 58, 5, 45, 147, 263, 321, 6, 81, 397, 1012, 1654, 1975, 7, 133, 933, 3341, 7340, 11290, 13265, 8, 204, 1962, 9637, 28333, 56278, 82808, 96073, 9, 297, 3776, 24758, 96313, 246905, 455534, 647680, 743753, 10, 415, 6767, 57678, 292092, 961897, 2227689, 3882510, 5370016, 6113769

Offset

0,2

Links

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

Formula

Conjecture: A(n,0) = A258173(n+1). - Mikhail Kurkov, Oct 27 2024

A(n,k) = A(n,k-1) + (A(n,k-1) - A(n-1,k))/k + k*A(n-1,k) + A(n-1,k+1) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = k+1. - Mikhail Kurkov, Nov 24 2024

Example

Array begins:
==============================================================
n\k|     0     1      2       3       4        5         6 ...
---+----------------------------------------------------------
0  |     1     2      3       4       5        6         7 ...
1  |     3     9     22      45      81      133       204 ...
2  |    12    46    147     397     933     1962      3776 ...
3  |    58   263   1012    3341    9637    24758     57678 ...
4  |   321  1654   7340   28333   96313   292092    800991 ...
5  |  1975 11290  56278  246905  961897  3357309  10601156 ...
6  | 13265 82808 455534 2227689 9749034 38415080 137251108 ...
  ...

Prog

(PARI)
A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, k)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-1, k, v[k+1] + k*sum(j=1, k, v[j])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(6) }

Crossrefs

Cf. A258173.

Sequence in context: A248788 A340914 A194232 * A110042 A306101 A364967

Adjacent sequences: A371564 A371565 A371566 * A371568 A371569 A371570

Keyword

nonn,tabl

Author

Mikhail Kurkov, Mar 28 2024

Status

approved