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A160990 Number of partitions of n where every part appears at least 20 times 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,40

LINKS

R. H. Hardin, Table of n, a(n) for n=1..1000

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

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

STATUS

approved

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)