A160989 Number of partitions of n where every part appears at least 19 times

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

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