A160990 - OEIS

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A160990

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

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 + 6c) exp(sqrt((2Pi^2/3 + 4c)n)) / (4sqrt(3)Pin), 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^(20k)/(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 March 20 22:57 EDT 2023. Contains 361392 sequences. (Running on oeis4.)