A023012 Number of partitions of n into parts of 14 kinds.

1, 14, 119, 770, 4165, 19754, 84602, 333608, 1228080, 4263770, 14071827, 44420796, 134793918, 394805110, 1119974875, 3086034350, 8280022023, 21678277754, 55486209625, 139065013640, 341779759755, 824753397814, 1956347387428

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: A241463 A284766 A341390 * A073383 A022642 A268446

Adjacent sequences: A023009 A023010 A023011 * A023013 A023014 A023015

Keyword

nonn

Author

David W. Wilson

Status

approved