A221835 G.f. satisfies: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (x + A(-x)^k).

1, 1, 1, 1, 2, 2, 5, 7, 23, 48, 190, 469, 2076, 5613, 27112, 80004, 415821, 1332560, 7380671, 25483465, 149401274, 552137511, 3408722899, 13414205244, 86845091349, 362317409552, 2451291749604, 10800354549538, 76134098052646, 353054546986058, 2586405677507199

Offset

0,5

Comments

Compare to the identity:

G(x) = Sum_{n>=0} x^n / Product_{k=1..n} (x + G(-k*x)) when G(x) = 1/(1-x).

Links

Table of n, a(n) for n=0..30.

Example

G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 + 5*x^6 + 7*x^7 + 23*x^8 +...
where
A(x) = 1 + x/(x+A(-x)) + x^2/((x+A(-x))*(x+A(-x)^2)) + x^3/((x+A(-x))*(x+A(-x)^2)*(x+A(-x)^3)) + x^4/((x+A(-x))*(x+A(-x)^2)*(x+A(-x)^3)*(x+A(-x)^4)) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/prod(k=1, m, x+subst(A^k, x, -x+x*O(x^n))) )); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A356434 A300439 A208818 * A074476 A224610 A265819

Adjacent sequences: A221832 A221833 A221834 * A221836 A221837 A221838

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2013

Status

approved