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A202203
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E.g.f.: Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1-x^k).
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1
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1, 1, 1, 5, 12, 74, 420, 2904, 19880, 210384, 1844640, 20910240, 242478720, 3193551360, 41853651840, 682405788960, 9824634892800, 173309920358400, 3095955573419520, 58684751375685120, 1111152812649062400, 24883693662159360000, 514031737571893094400
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OFFSET
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0,4
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LINKS
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EXAMPLE
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E.g.f.: A(x) = 1 + x + x^2/2! + 5*x^3/3! + 12*x^4/4! + 74*x^5/5! +...
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! +...
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PROG
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(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)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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