A306026 - OEIS

%I #8 Jun 17 2018 13:52:58

%S 1,1,2,5,16,66,343,2180,16505,145773,1477880,16986349,219158316,

%T 3147962668,49982588535,871766923048,16609804758449,344016348602845,

%U 7711752589539436,186379711851775401,4839449174872615116,134575228738532130948,3996183953610068510929

%N Antidiagonal sums of A306024.

%H Alois P. Heinz, <a href="/A306026/b306026.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = Sum_{j=0..n} j! * [x^j] exp(Sum_{i=1..n-j} (exp(i*x)-1)/i).

%F a(n) = Sum_{j=0..n} A306024(j,n-j).

%p b:= proc(n, k, m) option remember; `if`(n=0, 1,

%p       add(b(n-1, k, max(m, j)), j=1..m+k))

%p     end:

%p a:= n-> add(b(j, n-j, 0), j=0..n):

%p seq(a(n), n=0..25);

%p # second Maple program:

%p b:= (n, k)-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..k)), x, n+1), x, n):

%p a:= n-> add(b(j, n-j), j=0..n):

%p seq(a(n), n=0..25);

%Y Cf. A306024, A305971.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 17 2018