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A306026 Antidiagonal sums of A306024.

%I A306026 #8 Jun 17 2018 13:52:58
%S A306026 1,1,2,5,16,66,343,2180,16505,145773,1477880,16986349,219158316,
%T A306026 3147962668,49982588535,871766923048,16609804758449,344016348602845,
%U A306026 7711752589539436,186379711851775401,4839449174872615116,134575228738532130948,3996183953610068510929
%N A306026 Antidiagonal sums of A306024.
%H A306026 Alois P. Heinz, <a href="/A306026/b306026.txt">Table of n, a(n) for n = 0..200</a>
%F A306026 a(n) = Sum_{j=0..n} j! * [x^j] exp(Sum_{i=1..n-j} (exp(i*x)-1)/i).
%F A306026 a(n) = Sum_{j=0..n} A306024(j,n-j).
%p A306026 b:= proc(n, k, m) option remember; `if`(n=0, 1,
%p A306026       add(b(n-1, k, max(m, j)), j=1..m+k))
%p A306026     end:
%p A306026 a:= n-> add(b(j, n-j, 0), j=0..n):
%p A306026 seq(a(n), n=0..25);
%p A306026 # second Maple program:
%p A306026 b:= (n, k)-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..k)), x, n+1), x, n):
%p A306026 a:= n-> add(b(j, n-j), j=0..n):
%p A306026 seq(a(n), n=0..25);
%Y A306026 Cf. A306024, A305971.
%K A306026 nonn
%O A306026 0,3
%A A306026 _Alois P. Heinz_, Jun 17 2018