login
A258311
Row sums of A258310.
2
1, 1, 3, 7, 26, 86, 392, 1660, 9065, 46705, 297984, 1805926, 13186497, 91788477, 754481662, 5924676900, 54092804430, 472512732558, 4739696836485, 45540919862179, 497377234156959, 5208759709993591, 61475622078245542, 696384168181553136, 8825761698420052542
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A258310(n,k).
MAPLE
b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
`if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (k*x+y)/y, 1)
+b(x-1, y, false, k) +b(x-1, y+1, true, k)))
end:
A:= (n, k)-> b(n, 0, false, k):
T:= proc(n, k) option remember;
add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
end:
a:= proc(n) option remember; add(T(n, k), k=0..n/2) end:
seq(a(n), n=0..30);
MATHEMATICA
b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0,
If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (k*x + y)/y, 1]
+ b[x - 1, y, False, k] + b[x - 1, y + 1, True, k]]];
A[n_, k_] := b[n, 0, False, k];
T[n_, k_] := Sum[A[n, i] (-1)^(k - i) Binomial[k, i], {i, 0, k}]/k!;
a[n_] := Sum[T[n, k], {k, 0, n/2}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 01 2022, after Alois P. Heinz *)
CROSSREFS
Cf. A258310.
Sequence in context: A148740 A148741 A328280 * A184459 A215018 A069738
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 25 2015
STATUS
approved