OFFSET
1,2
LINKS
Max Alekseyev, Proof of the conjecture
FORMULA
Conjecture: G.f. is x/(1-x)+((1-x^12)/((1-x^2)*(1-x^5)))*(1/Product_{k>0} (1-x^(prime(k)+1))), i.e. a(n) = 1 + number of partitions of n into parts of the form p+1, p a prime, excluding 12 and including 2 and 5. Added May 28 2008: The conjecture is correct! See the link. - Max Alekseyev
MAPLE
A139807 := proc(n) local g, i, p ; g := (1-x^12)/(1-x^2)/(1-x^5) ; for i from 1 do p := ithprime(i) ; if p > n then break ; fi ; g := taylor(g/(1-x^(p+1)), x=0, n+1) ; od: coeftayl( g+1/(1-x), x=0, n) ; end: seq(A139807(n), n=1..80) ; # R. J. Mathar, May 29 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, May 23 2008
EXTENSIONS
More terms from R. J. Mathar, May 29 2008
STATUS
approved