VOOZH about

URL: https://oeis.org/A391838

⇱ A391838 - OEIS

login
A391838
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-x^2)/x) ).
2
1, 1, 2, 9, 72, 760, 9900, 156240, 2903040, 61943616, 1492545600, 40100860800, 1188788166720, 38545430489280, 1357015343523840, 51552166609944000, 2102033431456358400, 91568267279987097600, 4244171627969701908480, 208553808697356690247680, 10829949151457933392896000
OFFSET
0,3
LINKS
FORMULA
E.g.f. A(x) satisfies A(x) = 1 - log(1-(x*A(x))^2)/(x*A(x)).
a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} 1/(2*k+1)! * |Stirling1(n-k,n-2*k)|/(n-k)!.
MATHEMATICA
Table[(n!)^2* Sum[1/(2*k+1)!*Abs[StirlingS1[n-k, n-2*k]/(n-k)!], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vincenzo Librandi, Feb 05 2026 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-log(1-x^2)/x))/x))
(Magma) [Factorial(n)^2 * &+[1/Factorial(2*k+1) * Abs(StirlingFirst(n - k, n-2*k) / Factorial(n - k)): k in [0..Floor(n/2)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 05 2026
CROSSREFS
Sequence in context: A370889 A367485 A392889 * A133941 A240956 A038035
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 25 2026
STATUS
approved