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A305597
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O.g.f. A(x) satisfies: 0 = [x^n] exp( n*(n-1) * x * A(x) ) / A(x), for n > 1, with A'(0) = 1.
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3
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1, 1, 3, 59, 1775, 71511, 3735265, 245211865, 19803108233, 1936950231585, 226553844824131, 31331105054010115, 5069552336811706983, 950370245531340684983, 204551803567400710962529, 50129834142929585060592433, 13883636379729966042468837937, 4315912911594085891292265635265, 1496719856496801168910452641821123, 575834703501821334832940981183532907
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OFFSET
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0,3
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COMMENTS
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It is remarkable that this sequence should consist entirely of integers.
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LINKS
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FORMULA
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a(n) ~ c * n^(2*n + 2) / exp(2*n), where c = 15.159858073932625358279885219043... - Vaclav Kotesovec, Aug 11 2021
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EXAMPLE
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O.g.f.: A(x) = 1 + x + 3*x^2 + 59*x^3 + 1775*x^4 + 71511*x^5 + 3735265*x^6 + 245211865*x^7 + 19803108233*x^8 + 1936950231585*x^9 + ...
RELATED SERIES.
A'(x)/A(x) = 1 + 5*x + 169*x^2 + 6857*x^3 + 348121*x^4 + 21952541*x^5 + 1688688793*x^6 + 156361635585*x^7 + 17247060489337*x^8 + ...
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PROG
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(PARI) {a(n) = my(A=[1, 1], m); for(i=1, n+1, m=#A; A=concat(A, 0); A[m+1] = Vec( exp(m*(m-1)*x*Ser(A)) / Ser(A) )[m+1] ); A[n+1]}
for(n=0, 20, print1(a(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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