OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..12000 (terms 1..5000 from Alois P. Heinz)
FORMULA
a(n) = A180681(2*n-1,n).
a(n) ~ exp(Pi*sqrt(2*n/3)) * n / (8*sqrt(3)). - Vaclav Kotesovec, May 27 2018
MAPLE
f:= n-> (n-1)*n/2:
b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n+f(n)],
b(n, i-1)+(p-> p+[0, p[1]*(n+f(i))])(b(n-i, min(n-i, i))))
end:
a:= n-> (p-> p[1]*(2*n-1+f(n))+p[2])(b(n-1$2)):
seq(a(n), n=1..45);
MATHEMATICA
f[n_] := n(n-1)/2;
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, {1, n + f[n]}, b[n, i - 1] + Function[p, p + {0, p[[1]] (n + f[i])}][b[n - i, Min[n - i, i]]]];
a[n_] := Function[p, p[[1]] (2n - 1 + f[n]) + p[[2]]][b[n - 1, n - 1]];
Array[a, 45] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 22 2018
STATUS
approved