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A258311 Row sums of A258310.

%I A258311 #8 May 01 2022 12:33:22
%S A258311 1,1,3,7,26,86,392,1660,9065,46705,297984,1805926,13186497,91788477,
%T A258311 754481662,5924676900,54092804430,472512732558,4739696836485,
%U A258311 45540919862179,497377234156959,5208759709993591,61475622078245542,696384168181553136,8825761698420052542
%N A258311 Row sums of A258310.
%H A258311 Alois P. Heinz, <a href="/A258311/b258311.txt">Table of n, a(n) for n = 0..500</a>
%F A258311 a(n) = Sum_{k=0..floor(n/2)} A258310(n,k).
%p A258311 b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
%p A258311       `if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (k*x+y)/y, 1)
%p A258311                   +b(x-1, y, false, k) +b(x-1, y+1, true, k)))
%p A258311     end:
%p A258311 A:= (n, k)-> b(n, 0, false, k):
%p A258311 T:= proc(n, k) option remember;
%p A258311        add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
%p A258311     end:
%p A258311 a:= proc(n) option remember; add(T(n, k), k=0..n/2) end:
%p A258311 seq(a(n), n=0..30);
%t A258311 b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0,
%t A258311      If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (k*x + y)/y, 1]
%t A258311                  + b[x - 1, y, False, k] + b[x - 1, y + 1, True, k]]];
%t A258311 A[n_, k_] := b[n, 0, False, k];
%t A258311 T[n_, k_] := Sum[A[n, i] (-1)^(k - i) Binomial[k, i], {i, 0, k}]/k!;
%t A258311 a[n_] := Sum[T[n, k], {k, 0, n/2}];
%t A258311 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 01 2022, after _Alois P. Heinz_ *)
%Y A258311 Cf. A258310.
%K A258311 nonn
%O A258311 0,3
%A A258311 _Alois P. Heinz_, May 25 2015