OFFSET
0,3
COMMENTS
a(n)^(1/n^2) / sqrt(n) tends to exp(1/4)/sqrt(2) = 0.907943... . - Vaclav Kotesovec, May 14 2016
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..36
FORMULA
a(n) = Sum_{k=n..n*(n+1)/2} A262072(k,n).
MAPLE
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
b(n, i-1) +`if`(i>n, 0, binomial(n, i)*b(n-i, i-1))))
end:
T:= (n, k)-> b(n, k) -`if`(k=0, 0, b(n, k-1)):
a:= n-> add(T(k, n), k=n..n*(n+1)/2):
seq(a(n), n=0..14);
MATHEMATICA
b[n_, i_] := b[n, i] = If[i*(i + 1)/2 < n, 0, If[n == 0, 1, b[n, i - 1] + If[i > n, 0, Binomial[n, i]*b[n - i, i - 1]]]];
T[n_, k_] := b[n, k] - If[k == 0, 0, b[n, k - 1]];
a[n_] := Sum[T[k, n], { k, n, n*(n + 1)/2}];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, May 24 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2015
STATUS
approved