cp's OEIS Frontend

A383410 Array read by downward antidiagonals: A(n,k) = Sum_{i=0..n-1} Sum_{j=0..k+1} binomial(n-1,i)*binomial(k+1,j)*A(i,j) with A(0,k) = 1, n >= 0, k >= 0.

%I A383410 #6 May 03 2025 19:02:22
%S A383410 1,1,2,1,4,8,1,8,22,44,1,16,62,154,308,1,32,178,554,1306,2612,1,64,
%T A383410 518,2038,5690,12994,25988,1,128,1522,7634,25366,66338,148282,296564,
%U A383410 1,256,4502,29014,115298,346366,867002,1908274,3816548,1,512,13378,111554,532726,1844042,5179798,12564434,27333706,54667412
%N A383410 Array read by downward antidiagonals: A(n,k) = Sum_{i=0..n-1} Sum_{j=0..k+1} binomial(n-1,i)*binomial(k+1,j)*A(i,j) with A(0,k) = 1, n >= 0, k >= 0.
%F A383410 Conjecture: A(n,0) = A005649(n).
%e A383410 Array begins:
%e A383410 ==================================================================
%e A383410 n\k|     0      1      2       3        4         5          6 ...
%e A383410 ---+--------------------------------------------------------------
%e A383410 0  |     1      1      1       1        1         1          1 ...
%e A383410 1  |     2      4      8      16       32        64        128 ...
%e A383410 2  |     8     22     62     178      518      1522       4502 ...
%e A383410 3  |    44    154    554    2038     7634     29014     111554 ...
%e A383410 4  |   308   1306   5690   25366   115298    532726    2495570 ...
%e A383410 5  |  2612  12994  66338  346366  1844042   9985054   54865658 ...
%e A383410 6  | 25988 148282 867002 5179798 31540898 195320182 1227693842 ...
%e A383410   ...
%o A383410 (PARI) A(m, n=m)={my(r=vectorv(m+1), v=vector(m+1, j, vector(n+m-j+2, k, (j==1)))); r[1] = v[1][1..n+1];
%o A383410 for(i=1, m, v[i+1] = vector(#v[i+1], k, sum(j=1, i, sum(q=1, k+1, binomial(i-1,j-1)*binomial(k,q-1)*v[j][q]))); r[1+i] = v[i+1][1..n+1]); Mat(r)}
%o A383410 { A(6) }
%Y A383410 Cf. A005649.
%K A383410 nonn,tabl
%O A383410 0,3
%A A383410 _Mikhail Kurkov_, Apr 26 2025