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A160989 Number of partitions of n where every part appears at least 19 times 1
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, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 8, 7, 8, 9, 9, 9, 11, 10, 11, 12, 14, 13, 15, 15, 17, 17, 18, 18, 21, 20, 21, 22, 24, 23, 25, 25, 27, 27, 28, 31, 32, 32, 33, 35, 38, 37, 38, 40, 42, 43, 43, 45 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,38

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(-19*x)) dx = -1.344968702391930099087979420509926453320910037193266189844... . - Vaclav Kotesovec, Jan 05 2016

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(19*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

CROSSREFS

Sequence in context: A160990 A347516 A322357 * A066788 A160988 A184319

Adjacent sequences:  A160986 A160987 A160988 * A160990 A160991 A160992

KEYWORD

nonn

AUTHOR

R. H. Hardin Jun 01 2009

STATUS

approved

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)