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A258308 Row sums of A258307.

%I A258308 #10 Apr 30 2022 12:56:55
%S A258308 1,1,3,7,24,74,277,997,4016,16029,68802,296740,1347175,6185975,
%T A258308 29530010,143008050,714469780,3625572745,18884279461,99936069760,
%U A258308 540947985741,2974463266900,16686653393208,95053009906135,551356966419818,3245644584299434,19425857465136193
%N A258308 Row sums of A258307.
%H A258308 Alois P. Heinz, <a href="/A258308/b258308.txt">Table of n, a(n) for n = 0..500</a>
%F A258308 a(n) = Sum_{k=0..floor(n/2)} A258307(n,k).
%p A258308 b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
%p A258308       `if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (x+k*y)/y, 1)
%p A258308                   +b(x-1, y, false, k) +b(x-1, y+1, true, k)))
%p A258308     end:
%p A258308 A:= (n, k)-> b(n, 0, false, k):
%p A258308 T:= proc(n, k) option remember;
%p A258308        add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
%p A258308     end:
%p A258308 a:= n-> add(T(n, k), k=0..n/2):
%p A258308 seq(a(n), n=0..30);
%t A258308 b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0, If[x == 0, 1,
%t A258308      b[x - 1, y - 1, False, k]*If[t, (x + k*y)/y, 1] +
%t A258308      b[x - 1, y, False, k] +
%t A258308      b[x - 1, y + 1, True, k]]];
%t A258308 A[n_, k_] := b[n, 0, False, k];
%t A258308 T[n_, k_] := T[n, k] =
%t A258308      Sum[A[n, i]*(-1)^(k-i)*Binomial[k, i], {i, 0, k}]/k!;
%t A258308 a[n_] := Sum[T[n, k], {k, 0, n/2}];
%t A258308 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 30 2022, after _Alois P. Heinz_ *)
%Y A258308 Cf. A258307.
%K A258308 nonn
%O A258308 0,3
%A A258308 _Alois P. Heinz_, May 25 2015