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A213236
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a(n) = (-n)^(n-1).
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2
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1, -2, 9, -64, 625, -7776, 117649, -2097152, 43046721, -1000000000, 25937424601, -743008370688, 23298085122481, -793714773254144, 29192926025390625, -1152921504606846976, 48661191875666868481, -2185911559738696531968, 104127350297911241532841
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f.: LambertW(x).
E.g.f. is the functional inverse of x * exp(x) which is the e.g.f. of A000027.
E.g.f. A(x) satisfies A(x) = x / exp(A(x)).
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EXAMPLE
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x - 2*x^2 + 9*x^3 - 64*x^4 + 625*x^5 - 7776*x^6 + 117649*x^7 + ...
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MAPLE
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a := proc(n); `if`( n<0, 0, n! * coeff( taylor( LambertW(x), x=0, n+1 ), x, n)); end;
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MATHEMATICA
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a[ n_] := If[ n < 0, 0, n! SeriesCoefficient[ ProductLog @ z, {z, 0, n}]]
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PROG
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(PARI) {a(n) = if( n<1, 0, (-n) ^ (n-1))}
(PARI) {a(n) = if( n<1, 0, n! * polcoeff( serreverse( x * exp(x + x * O(x^n))), n))}
(PARI) {a(n) = local(A); if( n<1, 0, A = O(x); for( k=1, n, A = x / exp(A)); n! * polcoeff( A, n))}
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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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