OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1006
FORMULA
From Vaclav Kotesovec, Mar 03 2026: (Start)
a(n) ~ 10^(n-2) / (8! * QPochhammer(1/10)).
G.f.: (1 - 45*x + 862*x^2 - 9177*x^3 + 59410*x^4 - 240065*x^5 + 596229*x^6 - 855652*x^7 + 613453*x^8 - 148329*x^9) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)*(1 - 10*x) * Product_{k>=1} (1 - x^k)). (End)
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
Stirling2(n, j), j=0..10), add(b(n-i*j, i-1), j=0..n/i))
end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 10}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
(* or *)
nmax = 40; CoefficientList[Series[(1 - 45*x + 862*x^2 - 9177*x^3 + 59410*x^4 - 240065*x^5 + 596229*x^6 - 855652*x^7 + 613453*x^8 - 148329*x^9) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)*(1 - 10*x) * Product[(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 03 2026 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2018
STATUS
approved
