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A023012 Number of partitions of n into parts of 14 kinds. 2
1, 14, 119, 770, 4165, 19754, 84602, 333608, 1228080, 4263770, 14071827, 44420796, 134793918, 394805110, 1119974875, 3086034350, 8280022023, 21678277754, 55486209625, 139065013640, 341779759755, 824753397814, 1956347387428 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010853. - Alois P. Heinz, Oct 17 2008

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

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

FORMULA

a(0) = 1, a(n) = (14/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

MAPLE

with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*14, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008

MATHEMATICA

CoefficientList[Series[1/QPochhammer[x]^14, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

PROG

(PARI) Vec(1/eta(x)^14 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

CROSSREFS

14th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A091303 A241463 A284766 * A073383 A022642 A268446

Adjacent sequences:  A023009 A023010 A023011 * A023013 A023014 A023015

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 23 15:58 EDT 2019. Contains 325258 sequences. (Running on oeis4.)