OFFSET
10,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 10..5000
FORMULA
a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-3))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-3)) / (4*4!*sqrt(12)*Pi*n). - Vaclav Kotesovec, Sep 18 2019
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
(t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(4):
seq(a(n), n=10..49);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[With[{t = n - i j}, b[t, Min[t, i - 1], k]], {j, 1, n/i}] k + b[n, i - 1, k]]];
a[n_] := With[{k = 4}, Sum[b[n, n, k-i] (-1)^i Binomial[k, i], {i, 0, k}]/ k!];
a /@ Range[10, 49] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2019
STATUS
approved