OFFSET
3,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..1000
FORMULA
a(n) ~ c * 3^n, where c = 1/(6*Product_{n>=1} (1-1/3^n)) = 1/(6*QPochhammer[1/3, 1/3]) = 1/(6*A100220) = 0.297552056999755698394581... . - Vaclav Kotesovec, Jun 01 2015
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
end:
T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 3):
seq(a(n), n=3..35);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k*b[n - i, i, k]]]];
T[n_, k_] := Sum[b[n, n, k - i]*(-1)^i/(i!*(k - i)!), {i, 0, k}];
a[n_] := T[n, 3];
Table[a[n], {n, 3, 35}] (* Jean-François Alcover, May 22 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 30 2015
STATUS
approved