cp's OEIS Frontend

A369292 Array read by downward antidiagonals: A(n,k) = -A(n-1,k) + (k+1)*A(n-1,k+1) + A(n-1,k+2) with A(0,k) = 1, n >= 0, k >= 0.

%I A369292 #15 Nov 24 2024 13:35:32
%S A369292 1,1,1,1,2,4,1,3,8,18,1,4,14,42,108,1,5,22,84,276,780,1,6,32,150,612,
%T A369292 2160,6600,1,7,44,246,1212,5220,19560,63840,1,8,58,378,2196,11280,
%U A369292 50880,200760,693840,1,9,74,552,3708,22260,118560,556920,2299920,8361360
%N A369292 Array read by downward antidiagonals: A(n,k) = -A(n-1,k) + (k+1)*A(n-1,k+1) + A(n-1,k+2) with A(0,k) = 1, n >= 0, k >= 0.
%e A369292 Array begins:
%e A369292 =====================================================
%e A369292 n\k|    0     1     2      3      4      5      6 ...
%e A369292 ---+-------------------------------------------------
%e A369292 0  |    1     1     1      1      1      1      1 ...
%e A369292 1  |    1     2     3      4      5      6      7 ...
%e A369292 2  |    4     8    14     22     32     44     58 ...
%e A369292 3  |   18    42    84    150    246    378    552 ...
%e A369292 4  |  108   276   612   1212   2196   3708   5916 ...
%e A369292 5  |  780  2160  5220  11280  22260  40800  70380 ...
%e A369292 6  | 6600 19560 50880 118560 252120 496920 919200 ...
%e A369292   ...
%o A369292 (PARI)
%o A369292 A(m,n=m)={my(r=vectorv(m+1), v=vector(n+2*m+1,k,1)); r[1] = v[1..n+1];
%o A369292 for(i=1, m, v=vector(#v-2, k, -v[k] + k*v[k+1] + v[k+2]); r[1+i] = v[1..n+1]); Mat(r)}
%o A369292 { A(6) } \\ _Andrew Howroyd_, Jan 24 2024
%Y A369292 Column k=0 is A144085.
%Y A369292 Rows n=0..2 are A000012, A000027(n+1), A014206(n+1).
%K A369292 nonn,tabl
%O A369292 0,5
%A A369292 _Mikhail Kurkov_, Jan 24 2024