cp's OEIS Frontend

A384788 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384787.

%I A384788 #11 Jun 10 2025 13:57:10
%S A384788 1,1,0,1,1,0,1,2,7,0,1,3,16,148,0,1,4,27,338,7381,0,1,5,40,576,16240,
%T A384788 801536,0,1,6,55,868,26829,1697602,186678019,0,1,7,72,1220,39424,
%U A384788 2701488,384962560,93865986880,0,1,8,91,1638,54325,3828164,595921743,190657584770,102755888482153,0
%N A384788 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384787.
%F A384788 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} 2^(n-j) * (n+k)^(j-1) * binomial(n,j) * A(n-j,j).
%e A384788 Square array begins:
%e A384788   1,      1,       1,       1,       1,       1, ...
%e A384788   0,      1,       2,       3,       4,       5, ...
%e A384788   0,      7,      16,      27,      40,      55, ...
%e A384788   0,    148,     338,     576,     868,    1220, ...
%e A384788   0,   7381,   16240,   26829,   39424,   54325, ...
%e A384788   0, 801536, 1697602, 2701488, 3828164, 5094400, ...
%o A384788 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, 2^(n-j)*(n+k)^(j-1)*binomial(n, j)*a(n-j, j)));
%Y A384788 Columns k=0..1 give A000007, A384787.
%Y A384788 Cf. A379168.
%K A384788 nonn,tabl
%O A384788 0,8
%A A384788 _Seiichi Manyama_, Jun 10 2025