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A160975 Number of partitions of n where every part appears at least 5 times. 2
0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 3, 3, 5, 4, 7, 7, 7, 8, 11, 12, 12, 14, 15, 16, 23, 20, 24, 26, 29, 36, 40, 40, 46, 50, 63, 63, 76, 76, 87, 103, 108, 117, 135, 140, 167, 173, 191, 205, 235, 257, 278, 300, 327, 354, 413, 424, 469, 511, 555, 616, 673, 711, 783, 849, 947 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

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

FORMULA

From Emeric Deutsch, Jun 28 2009: (Start)

G.f.: Product_{j>=1} (1+x^(5*j)/(1-x^j)).

(End)

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(-5*x)) dx = -0.990807844177842472956484606320623872921836802804155824925... . - Vaclav Kotesovec, Jan 05 2016

EXAMPLE

From Emeric Deutsch, Jun 28 2009: (Start)

a(15)=3 because we have 33333, 2222211111, and 1^(15).

(End)

MAPLE

g := product(1+x^(5*j)/(1-x^j), j = 1..20): gser := series(g, x = 0, 80): seq(coeff(gser, x, n), n = 1..75); # Emeric Deutsch, Jun 28 2009

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(5*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

CROSSREFS

Cf. A007690, A100405, A160974, A160976-A160990.

Sequence in context: A161080 A161296 A161271 * A305300 A330241 A175851

Adjacent sequences:  A160972 A160973 A160974 * A160976 A160977 A160978

KEYWORD

nonn

AUTHOR

R. H. Hardin Jun 01 2009

EXTENSIONS

Initial terms changed to match b-file. - N. J. A. Sloane, Aug 31 2009

Maple program fixed by Vaclav Kotesovec, Nov 28 2015

STATUS

approved

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Last modified September 28 15:31 EDT 2021. Contains 347716 sequences. (Running on oeis4.)