cp's OEIS Frontend

A384761 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 A384760.

%I A384761 #11 Jun 09 2025 10:33:31
%S A384761 1,1,0,1,-1,0,1,-2,1,0,1,-3,4,5,0,1,-4,9,4,-35,0,1,-5,16,-9,-104,-281,
%T A384761 0,1,-6,25,-40,-171,-112,5671,0,1,-7,36,-95,-176,717,14164,42671,0,1,
%U A384761 -8,49,-180,-35,2176,20619,-18104,-2179127,0
%N A384761 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 A384760.
%F A384761 A(n,0) = 0^n; A(n,k) = (-1)^n * k * Sum_{j=0..n} (n+k)^(j-1) * binomial(n,j) * A(n-j,j).
%e A384761 Square array begins:
%e A384761   1,    1,    1,    1,    1,    1, ...
%e A384761   0,   -1,   -2,   -3,   -4,   -5, ...
%e A384761   0,    1,    4,    9,   16,   25, ...
%e A384761   0,    5,    4,   -9,  -40,  -95, ...
%e A384761   0,  -35, -104, -171, -176,  -35, ...
%e A384761   0, -281, -112,  717, 2176, 3875, ...
%o A384761 (PARI) a(n, k) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n+k)^(j-1)*binomial(n, j)*a(n-j, j)));
%Y A384761 Columns k=0..1 give A000007, A384760.
%Y A384761 Cf. A379168.
%K A384761 sign,tabl
%O A384761 0,8
%A A384761 _Seiichi Manyama_, Jun 09 2025