A168268 G.f.: exp( Sum_{n>=1} A007837(n)*x^n/n ), where A007837(n) = number of partitions of n-set with distinct block sizes.

1, 1, 1, 2, 3, 6, 20, 45, 116, 385, 2224, 6396, 23708, 88065, 445784, 3962502, 14478825, 64495508, 309085415, 1608099881, 10856426344, 142802148953, 604464533847, 3324499738872, 17795211310951, 112537384959231, 718232376832560

Offset

0,4

Comments

Conjectured to consist entirely of integers.

Links

Table of n, a(n) for n=0..26.

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 20*x^6 + 45*x^7 +...
log(A(x)) = x + x^2/2 + 4*x^3/3 + 5*x^4/4 + 16*x^5/5 + 82*x^6/6 + 169*x^7/7 + 541*x^8/8 +...+ A007837(n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(serlaplace(intformal((-1+prod(k=1, n+1, 1+x^k/k! +x^2*O(x^n)))/x))), n)}

Crossrefs

Cf. A007837.

Sequence in context: A227316 A176806 A323464 * A340652 A361648 A277876

Adjacent sequences: A168265 A168266 A168267 * A168269 A168270 A168271

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2011

Status

approved