cp's OEIS Frontend

A370381 Array read by downward antidiagonals: A(n,k) = Sum_{j=0..k+1} binomial(k+2, j+1)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.

%I A370381 #15 Nov 25 2024 08:31:34
%S A370381 1,1,3,1,7,13,1,15,45,71,1,31,145,319,461,1,63,453,1355,2525,3447,1,
%T A370381 127,1393,5623,13241,22199,29093,1,255,4245,23051,68261,138219,215157,
%U A370381 273343,1,511,12865,93799,348761,850031,1549889,2282639,2829325,1,1023,38853,379835,1771925,5193867,11065437,18672307,26340253,31998903
%N A370381 Array read by downward antidiagonals: A(n,k) = Sum_{j=0..k+1} binomial(k+2, j+1)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.
%F A370381 Conjecture: A(n,0) = A003319(n+2). - _Mikhail Kurkov_, Oct 27 2024
%e A370381 Array begins:
%e A370381 ==================================================
%e A370381 n\k|    0     1      2      3       4        5 ...
%e A370381 ---+----------------------------------------------
%e A370381 0  |    1     1      1      1       1        1 ...
%e A370381 1  |    3     7     15     31      63      127 ...
%e A370381 2  |   13    45    145    453    1393     4245 ...
%e A370381 3  |   71   319   1355   5623   23051    93799 ...
%e A370381 4  |  461  2525  13241  68261  348761  1771925 ...
%e A370381 5  | 3447 22199 138219 850031 5193867 31604159 ...
%e A370381   ...
%o A370381 (PARI)
%o A370381 A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 1)); r[1] = v[1..n+1];
%o A370381 for(i=1, m, v=vector(#v-1, k, sum(j=1, k+1, binomial(k+1, j)*v[j])); r[1+i] = v[1..n+1]); Mat(r)}
%o A370381 { A(5) }
%Y A370381 Cf. A003319.
%K A370381 nonn,tabl
%O A370381 0,3
%A A370381 _Mikhail Kurkov_, Feb 17 2024