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A300455
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Logarithmic transform of the triangular numbers A000217.
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3
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0, 1, 2, -1, -11, 19, 201, -764, -7426, 52137, 448435, -5377604, -38712486, 777663613, 4258812299, -149524753650, -505685566184, 36733876797025, 30910872539763, -11174584391207360, 25170998506744790, 4101787001153848461, -24862093152821214653, -1776483826032814964966
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
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FORMULA
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E.g.f.: log(1 + exp(x)*x*(x + 2)/2).
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EXAMPLE
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E.g.f.: A(x) = x/1! + 2*x^2/2! - x^3/3! - 11*x^4/4! + 19*x^5/5! + 201*x^6/6! - 764*x^7/7! - 7426*x^8/8! + ...
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MAPLE
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a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*
binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->i*(i+1)/2)
end:
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Log[1 + Exp[x] x (x + 2)/2], {x, 0, nmax}], x] Range[0, nmax]!
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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