OFFSET
1,2
COMMENTS
a(n) = number of indecomposable partitions (A074664) of [n+3] in which n+3 lies in a doubleton block (see Link). - David Callan, Oct 08 2014
LINKS
FORMULA
L.g.f.: log( Sum_{n>=0} x^n / Product_{k=1..n} (1 - k*x) ).
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 39*x^4/4 + 171*x^5/5 + 822*x^6/6 +...
where exponentiation yields the o.g.f. of the Bell numbers:
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 52*x^5 + 203*x^6 + 877*x^7 +...
which equals the series:
exp(L(x)) = 1 + x/(1-x) + x^2/((1-x)*(1-2*x)) + x^3/((1-x)*(1-2*x)*(1-3*x)) +...
PROG
(PARI) {a(n)=n*polcoeff(log(sum(m=0, n, x^m/prod(k=1, m, 1-k*x +x*O(x^n)))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 28 2012
STATUS
approved