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A202203 E.g.f.: Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1-x^k). 1

%I

%S 1,1,1,5,12,74,420,2904,19880,210384,1844640,20910240,242478720,

%T 3193551360,41853651840,682405788960,9824634892800,173309920358400,

%U 3095955573419520,58684751375685120,1111152812649062400,24883693662159360000,514031737571893094400

%N E.g.f.: Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1-x^k).

%H Vaclav Kotesovec, <a href="/A202203/b202203.txt">Table of n, a(n) for n = 0..390</a>

%e E.g.f.: A(x) = 1 + x + x^2/2! + 5*x^3/3! + 12*x^4/4! + 74*x^5/5! +...

%e A(x) = 1 - log(1-x) + log(1-x)*log(1-x^2)/2! - log(1-x)*log(1-x^2)*log(1-x^3)/3! + log(1-x)*log(1-x^2)*log(1-x^3)*log(1-x^4)/4! +...

%o (PARI) {a(n)=n!*polcoeff(1+sum(m=1, sqrt(2*n+1), (1/m!)*prod(k=1, m, -log(1-x^k +x*O(x^n)))), n)}

%Y Cf. A191461.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Dec 14 2011

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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)