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%I #9 Apr 21 2024 22:11:51
%S 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 611,2169,7696,27913,1,65,404,1727,6695,25480,98093,386906,1,129,1050,
%U 5099,21573,87964,358993,1490687,6346119,1,257,2828,15647,72287,315688
%N Array read by 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.
%e Array begins:
%e =============================================================
%e n\k| 0 1 2 3 4 5 6 ...
%e ---+---------------------------------------------------------
%e 0 | 1 1 1 1 1 1 1 ...
%e 1 | 2 3 5 9 17 33 65 ...
%e 2 | 7 14 30 68 162 404 1050 ...
%e 3 | 37 89 227 611 1727 5099 15647 ...
%e 4 | 264 737 2169 6695 21573 72287 251109 ...
%e 5 | 2433 7696 25480 87964 315688 1174756 4522480 ...
%e 6 | 27913 98093 358993 1364681 5376121 21901073 92076673 ...
%e ...
%o (PARI)
%o A(m, n=m)={my(r=vectorv(m+1), v=vector(n+2*m+1, k, 1)); r[1] = v[1..n+1];
%o 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 { A(6) }
%Y Column k=0 is A135920 (without initial term and with different offset).
%K nonn,tabl
%O 0,3
%A _Mikhail Kurkov_, Jan 27 2024 [verification needed]
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