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A023014 Number of partitions of n into parts of 16 kinds. 2
1, 16, 152, 1088, 6460, 33440, 155584, 663936, 2636326, 9845040, 34861152, 117809728, 381946360, 1193074144, 3603543040, 10556065152, 30068145905, 83466484112, 226236086512, 599785472000, 1557643542308, 3967888347232, 9926348625408, 24413219138816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010855. - Alois P. Heinz, Oct 17 2008

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)^16.

a(0) = 1, a(n) = (16/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*16, 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]^16, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

PROG

(PARI) Vec(1/eta(x)^16 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

CROSSREFS

Cf. 16th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A049351 A240424 A225915 * A073384 A022644 A297090

Adjacent sequences:  A023011 A023012 A023013 * A023015 A023016 A023017

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)