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A379460 Array read by downward antidiagonals: A(n,k) = A(n,k-1) + (k+1)*(A(n-1,k) + A(n-1,k+1)) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = 1, n >= 0, k >= 0.

%I A379460 #4 Jan 03 2025 02:03:31
%S A379460 1,1,2,1,6,8,1,12,44,52,1,20,140,420,472,1,30,340,1860,5032,5504,1,42,
%T A379460 700,6020,28672,72912,78416,1,56,1288,15960,116592,508704,1241648,
%U A379460 1320064,1,72,2184,36792,380352,2496480,10257200,24317760,25637824,1,90,3480,76440,1059744,9696960,59030960,232182240,538637824,564275648
%N A379460 Array read by downward antidiagonals: A(n,k) = A(n,k-1) + (k+1)*(A(n-1,k) + A(n-1,k+1)) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = 1, n >= 0, k >= 0.
%F A379460 Conjecture: A(n,0) = A006351(n+1).
%e A379460 Array begins:
%e A379460 =============================================================
%e A379460 n\k|     0       1        2        3         4          5 ...
%e A379460 ---+---------------------------------------------------------
%e A379460 0  |     1       1        1        1         1          1 ...
%e A379460 1  |     2       6       12       20        30         42 ...
%e A379460 2  |     8      44      140      340       700       1288 ...
%e A379460 3  |    52     420     1860     6020     15960      36792 ...
%e A379460 4  |   472    5032    28672   116592    380352    1059744 ...
%e A379460 5  |  5504   72912   508704  2496480   9696960   31778208 ...
%e A379460   ...
%o A379460 (PARI) A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 1)); r[1] = v[1..n+1];
%o A379460 for(i=1, m, v[1] = v[1] + v[2]; for(k=2, #v-1, v[k] = v[k-1] + k*(v[k] + v[k+1])); r[1+i] = v[1..n+1]); Mat(r)}
%o A379460 { A(5) }
%Y A379460 Cf. A006351.
%K A379460 nonn,tabl
%O A379460 0,3
%A A379460 _Mikhail Kurkov_, Dec 23 2024