A334262 E.g.f. A(x) satisfies: A(x) = 2 * x / (exp(A(x)) * (2 + A(x))).

1, -3, 21, -235, 3630, -71631, 1721671, -48804183, 1594177605, -58963348675, 2435865852156, -111169287046467, 5554808694622369, -301609325982387255, 17682700497003095625, -1113293610926803531951, 74915504280675843548274, -5365793673423031533999147

Offset: 1

Author

Ilya Gutkovskiy, Apr 20 2020

Keywords

• sign

Comments

Exponential reversion of A000217 (triangular numbers).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..200
• Index entries for reversions of series

Crossrefs

Cf. A000217, A066399, A179848.

Programs

Mathematica

nmax = 18; CoefficientList[InverseSeries[Series[Exp[x] (x + x^2/2), {x, 0, nmax}], x], x] Range[0, nmax]! // Rest

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

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