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A027344 Number of partitions of n that do not contain 10 as a part. 3
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 75, 98, 130, 169, 220, 282, 363, 460, 585, 736, 925, 1154, 1440, 1782, 2205, 2713, 3333, 4075, 4977, 6050, 7347, 8888, 10735, 12925, 15541, 18627, 22297, 26620, 31734, 37741, 44825, 53118, 62865 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..44.

FORMULA

G.f.: (1-x^10) Product_{m>0} 1/(1-x^m).

a(n) = A000041(n)-A000041(n-10).

a(n) ~ 5*Pi * exp(sqrt(2*n/3)*Pi) / (6*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 10*Pi/(2*sqrt(6)))/sqrt(n) + (121/8 + 9/(2*Pi^2) + 19441*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

MAPLE

A41:= n-> `if`(n<0, 0, combinat[numbpart](n)):

a:= n-> A41(n) -A41(n-10):

seq(a(n), n=0..50);

CROSSREFS

10th column of A175788. Cf. A000041, A027336, A027337-A027343.

Sequence in context: A039905 A036009 A261776 * A184645 A053691 A242696

Adjacent sequences:  A027341 A027342 A027343 * A027345 A027346 A027347

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Benoit Cloitre, Dec 10 2002

Edited by Alois P. Heinz, Dec 04 2010

STATUS

approved

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Last modified July 28 13:15 EDT 2021. Contains 346332 sequences. (Running on oeis4.)