[go: up one dir, main page]

login
A023014
Number of partitions of n into parts of 16 kinds.
3
1, 16, 152, 1088, 6460, 33440, 155584, 663936, 2636326, 9845040, 34861152, 117809728, 381946360, 1193074144, 3603543040, 10556065152, 30068145905, 83466484112, 226236086512, 599785472000, 1557643542308, 3967888347232, 9926348625408, 24413219138816
OFFSET
0,2
COMMENTS
a(n) is Euler transform of A010855. - Alois P. Heinz, Oct 17 2008
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: A240424 A341391 A225915 * A073384 A022644 A297090
KEYWORD
nonn
STATUS
approved