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A334262 - OEIS
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A334262
E.g.f. A(x) satisfies: A(x) = 2 * x / (exp(A(x)) * (2 + A(x))).
1
1, -3, 21, -235, 3630, -71631, 1721671, -48804183, 1594177605, -58963348675, 2435865852156, -111169287046467, 5554808694622369, -301609325982387255, 17682700497003095625, -1113293610926803531951, 74915504280675843548274, -5365793673423031533999147
OFFSET
1,2
COMMENTS
Exponential reversion of A000217 (triangular numbers).
FORMULA
a(n) ~ -(-1)^n * n^(n-1) / (2^(1/4) * (sqrt(2)-1)^(n - 1/2) * exp(n*(sqrt(2)-1))). - Vaclav Kotesovec, Apr 21 2020
MATHEMATICA
nmax = 18; CoefficientList[InverseSeries[Series[Exp[x] (x + x^2/2), {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
PROG
(PARI) seq(n)= Vec(serlaplace(serreverse(sum(k=1, n, (k*(k+1)/2)*x^k/k!) + O(x*x^n)))); \\ Michel Marcus, Apr 21 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 20 2020
STATUS
approved