OFFSET
0,2
LINKS
P. C. P. Bhatt, An interesting way to partition a number, Inform. Process. Lett., 71, 1999, 141-148.
W. M. Y. Goh, P. Hitczenko and A. Shokoufandeh, s-partitions, Inform. Process. Lett., 82, 2002, 327-329.
FORMULA
a(n) = sum(k*A117145(n,k), k=1..n).
G.f.: sum(x^(2^k-1)/(1-x^(2^k-1)), k=1..infinity)/product(1-x^(2^k-1), k=1..infinity).
EXAMPLE
a(7)=16 because the s-partitions of 7 are [7],[3,3,1],[3,1,1,1,1] and [1,1,1,1,1,1,1], with a total of 1+3+5+7=16 parts.
MAPLE
g:=sum(x^(2^k-1)/(1-x^(2^k-1)), k=1..10)/product(1-x^(2^k-1), k=1..10): gser:=series(g, x=0, 60): seq(coeff(gser, x^n), n=1..56);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Mar 06 2006
STATUS
approved