A160990 Number of partitions of n where every part appears at least 20 times.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 4, 4, 5, 4, 7, 5, 7, 7, 8, 7, 10, 8, 10, 10, 11, 10, 13, 11, 15, 14, 15, 15, 19, 16, 19, 19, 21, 20, 23, 21, 25, 24, 25, 25, 29, 26, 29, 29, 34, 31, 35, 33, 38, 38, 39, 38, 44

Offset

0,41

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..1000 from R. H. Hardin)

Formula

a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-20*x)) dx = -1.354168532835449099374593344112387373408094711414623392193... . - Vaclav Kotesovec, Jan 05 2016

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+add(b(n-i*j, i-1), j=20..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..108);  # Alois P. Heinz, Feb 06 2024

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(20*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A167966 A348998 A167967 * A347516 A322357 A160989

Adjacent sequences: A160987 A160988 A160989 * A160991 A160992 A160993

Keyword

nonn

Author

R. H. Hardin, Jun 01 2009

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 06 2024

Status

approved