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A008639 Number of partitions of n into at most 10 parts. 5
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 128, 164, 212, 267, 340, 423, 530, 653, 807, 984, 1204, 1455, 1761, 2112, 2534, 3015, 3590, 4242, 5013, 5888, 6912, 8070, 9418, 10936, 12690, 14663, 16928, 19466, 22367, 25608, 29292, 33401, 38047 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n > 9: also number of partitions of n into parts <= 10: a(n) = A026820(n, 10). - Reinhard Zumkeller, Jan 21 2010

REFERENCES

A. Cayley, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 10, p. 415.

H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 2.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 359

Index entries for related partition-counting sequences

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 1, 1, 1, 2, 0, 0, -1, -1, -1, -1, -3, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, -3, -1, -1, -1, -1, 0, 0, 2, 1, 1, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, 1, -1).

FORMULA

G.f.: 1/(Product_{k=1..10} 1-x^k ). - David Neil McGrath, Apr 29 2015

a(n) = a(n-10) + A008638(n). - Vladimír Modrák, Sep 29 2020

MATHEMATICA

CoefficientList[ Series[ 1/ Product[ 1 - x^n, {n, 1, 10} ], {x, 0, 60} ], x ]

PROG

(PARI) Vec(1/prod(k=1, 10, 1-x^k)+O(x^99)) \\ Charles R Greathouse IV, May 06 2015

CROSSREFS

Essentially same as A026816.

a(n) = A008284(n + 10, 10), n >= 0.

Cf. A266778 (first differences), A288345 (partial sums).

Sequence in context: A242696 A218510 A026816 * A341914 A008633 A238868

Adjacent sequences:  A008636 A008637 A008638 * A008640 A008641 A008642

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)