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A023005 Number of partitions of n into parts of 6 kinds. 2
1, 6, 27, 98, 315, 918, 2492, 6372, 15525, 36280, 81816, 178794, 380051, 788004, 1597725, 3174210, 6190182, 11867310, 22395359, 41650050, 76413078, 138421358, 247783113, 438616728, 768291650, 1332444330, 2289213495, 3898064226, 6581591157, 11023247880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010722. - Alois P. Heinz, Oct 17 2008

REFERENCES

P Nataf, M Lajkó, A Wietek, K Penc, F Mila, AM Läuchli, Chiral spin liquids in triangular lattice SU (N) fermionic Mott insulators with artificial gauge fields, arXiv preprint arXiv:1601.00958, 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

N. J. A. Sloane, Transforms

FORMULA

G.f.: Product_{m>=1} 1/(1-x^m)^6.

a(n) ~ exp(2 * Pi * sqrt(n)) / (16 * n^(9/4)). - Vaclav Kotesovec, Feb 28 2015

MAPLE

with(numtheory): a:=proc(n) option remember; `if`(n=0, 1, add(add(d*6, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008

MATHEMATICA

nmax=50; CoefficientList[Series[Product[1/(1-x^k)^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)

CROSSREFS

Cf. 6th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A182821 A277283 A160533 * A001874 A009061 A012320

Adjacent sequences:  A023002 A023003 A023004 * A023006 A023007 A023008

KEYWORD

nonn,changed

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 8 06:50 EST 2016. Contains 278902 sequences.