cp's OEIS Frontend

A369595 Array read by downward antidiagonals: A(n,k) = A(n-1,k+2) + Sum_{j=0..k} binomial(k,j)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.

%I A369595 #20 Nov 25 2024 04:58:01
%S A369595 1,1,2,1,3,7,1,5,14,37,1,9,30,89,264,1,17,68,227,737,2433,1,33,162,
%T A369595 611,2169,7696,27913,1,65,404,1727,6695,25480,98093,386906,1,129,1050,
%U A369595 5099,21573,87964,358993,1490687,6346119,1,257,2828,15647,72287,315688,1364681,5959213,26542518,121159373
%N A369595 Array read by downward antidiagonals: A(n,k) = A(n-1,k+2) + Sum_{j=0..k} binomial(k,j)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.
%F A369595 Conjecture: A(n,0) = A135920(n+1). - _Mikhail Kurkov_, Oct 27 2024
%e A369595 Array begins:
%e A369595 =============================================================
%e A369595 n\k|     0     1      2       3       4        5        6 ...
%e A369595 ---+---------------------------------------------------------
%e A369595 0  |     1     1      1       1       1        1        1 ...
%e A369595 1  |     2     3      5       9      17       33       65 ...
%e A369595 2  |     7    14     30      68     162      404     1050 ...
%e A369595 3  |    37    89    227     611    1727     5099    15647 ...
%e A369595 4  |   264   737   2169    6695   21573    72287   251109 ...
%e A369595 5  |  2433  7696  25480   87964  315688  1174756  4522480 ...
%e A369595 6  | 27913 98093 358993 1364681 5376121 21901073 92076673 ...
%e A369595   ...
%o A369595 (PARI)
%o A369595 A(m, n=m)={my(r=vectorv(m+1), v=vector(n+2*m+1, k, 1)); r[1] = v[1..n+1];
%o A369595 for(i=1, m, v=vector(#v-2, k, v[k+2] + sum(j=1, k, binomial(k-1, j-1)*v[j])); r[1+i] = v[1..n+1]); Mat(r)}
%o A369595 { A(6) }
%Y A369595 Cf. A135920.
%K A369595 nonn,tabl
%O A369595 0,3
%A A369595 _Mikhail Kurkov_, Jan 27 2024