OFFSET
1,2
LINKS
J. S. Dowker, Relations between the Ehrhart polynomial, the heat kernel and Sylvester waves, arXiv:1108.1760 [math.NT], 2011. (See the factor in formula (27).)
G. J. Rieger, Über Partitionen, Mathematische Annalen (1959), Volume: 138, page 356-362. (See Satz 1.)
J. J. Sylvester, On the partition of numbers, Quarterly J. Pure Appl. Math. 1857, 1:141-152.
FORMULA
a(n) = denominator(W(n))/(n!*(n - 1)!) where W(n) = [t^(-1)] exp(t*x)/ Product_{k=1..n}(1 - exp(-t*k)).
MAPLE
read(PARTITIONS): # From the paper of Sills & Zeilberger cited in A375252.
a := n -> denom(op(pmnPC(n, x)[1])) / (n!*(n - 1)!):
seq(a(n), n = 1..54);
# Or, standalone:
W := proc(n) local k; exp(t*x)/mul(1 - exp(-t*k), k=1..n);
expand(series(%, t, n+1)); coeff(%, t, -1) end:
a := n -> n*denom(W(n))/(n!^2): seq(a(n), n = 1..24);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 09 2024
STATUS
approved