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 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Conjectured to consist entirely of integers. LINKS 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: A173744 A227316 A176806 * A002078 A000372 A123930 Adjacent sequences:  A168265 A168266 A168267 * A168269 A168270 A168271 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 05 2011 STATUS approved

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