OFFSET
0,3
COMMENTS
Equals row sums of triangle A104382. Asymptotics: a(n) ~ exp(Pi*sqrt((n^2+n)/6))/(2*6^(1/4))/(n^2+n)^(3/4).
REFERENCES
Abramowitz, M. and Stegun, I. A. (Editors). "Partitions into Distinct Parts." S24.2.2 in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 9th printing. New York: Dover, pp. 825-826, 1972.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, Partition Function Q.
FORMULA
Limit_{n-->inf} a(n+1)/a(n) = exp(sqrt(Pi^2/6)) = 3.605822247984...
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
`if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
end:
a:= n-> b(n*(n+1)/2):
seq(a(n), n=0..30); # Alois P. Heinz, Nov 24 2016
MATHEMATICA
Join[{1}, PartitionsQ/@Accumulate[Range[30]]] (* Harvey P. Dale, Dec 29 2012 *)
PROG
(PARI) {a(n)=polcoeff(prod(k=1, n*(n+1)/2, 1+x^k, 1+x*O(x^(n*(n+1)/2))), n*(n+1)/2)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 04 2005
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Aug 05 2016
STATUS
approved