cp's OEIS Frontend

A305971 Antidiagonal sums of A305962.

%I A305971 #14 Nov 16 2022 06:54:03
%S A305971 1,2,3,5,11,34,141,736,4653,34842,303848,3041514,34520903,439820187,
%T A305971 6238591638,97832195694,1685800545944,31746373299029,650170193047230,
%U A305971 14418116545259245,344857160229381442,8865220175506008295,244158955254595904415,7183277314615065192163
%N A305971 Antidiagonal sums of A305962.
%H A305971 Alois P. Heinz, <a href="/A305971/b305971.txt">Table of n, a(n) for n = 0..200</a>
%F A305971 a(n) = Sum_{j=0..n} (j-1)! * [x^(j-1)] exp(x + Sum_{i=1..n-j} (exp(i*x)-1)/i) for n > 0, a(0) = 1.
%F A305971 a(n) = Sum_{j=0..n} A305962(j,n-j).
%p A305971 b:= proc(n, k, m) option remember; `if`(n=0, 1,
%p A305971       add(b(n-1, k, max(m, j)), j=1..m+k))
%p A305971     end:
%p A305971 a:= n-> add(b(j, n-j, 1+j-n), j=0..n):
%p A305971 seq(a(n), n=0..25);
%p A305971 # second Maple program:
%p A305971 b:= (n, k)-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305971               (exp(j*x)-1)/j, j=1..k)), x, n), x, n-1)):
%p A305971 a:= n-> add(b(j, n-j), j=0..n):
%p A305971 seq(a(n), n=0..25);
%t A305971 b[n_, k_, m_] := b[n, k, m] = If[n == 0, 1, Sum[b[n - 1, k, Max[m, j]], {j, 1, m + k}]];
%t A305971 a[n_] := Sum[b[j, n - j, 1 + j - n], {j, 0, n}];
%t A305971 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Nov 16 2022, after _Alois P. Heinz_ *)
%Y A305971 Cf. A305962, A306026.
%K A305971 nonn
%O A305971 0,2
%A A305971 _Alois P. Heinz_, Jun 15 2018