OFFSET
0,4
LINKS
Robert Israel, Table of n, a(n) for n = 0..450
FORMULA
E.g.f.: exp( -Sum{k >= 1} x^k/A110654(k) ).
a(0) = 1; a(n) = -(n-1)! * Sum_{k=1..n} k/A110654(k) * a(n-k)/(n-k)!.
a(n) ~ -(-1)^n * n! / n^2 * (1 - 2*log(n)/n). - Vaclav Kotesovec, May 09 2022
MAPLE
S:=series((1-x^2)^(1+1/x), x, 31):
seq(coeff(S, x, i)*i!, i=0..30); # Robert Israel, Nov 01 2022
MATHEMATICA
nmax = 25; CoefficientList[Series[(1 - x^2)^(1 + 1/x), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 09 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2)^(1+1/x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, x^k/((k+1)\2)))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-(i-1)!*sum(j=1, i, j/((j+1)\2)*v[i-j+1]/(i-j)!)); v;
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 30 2022
STATUS
approved