A375832 E.g.f. satisfies A(x) = 1/(1 + x*log(1 - x^2*A(x))).

1, 0, 0, 6, 0, 60, 1440, 1680, 100800, 1905120, 9979200, 427109760, 8103110400, 102745843200, 3926897694720, 84531807360000, 1844343928627200, 69047821979136000, 1790206583413248000, 54550224714585600000, 2112795340044060672000

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-k)! * |Stirling1(k,n-2*k)|/( k! * (k+1)! ).

a(n) ~ sqrt(s*(-1 + s*(1 + r^2 + r^2*(-1 + 2*r)*s))/(1 + 2*r*s)) * n^(n-1) / (exp(n) * r^(n+1)), where r = 0.555108855597239653157700556001479889170962... and s = 1.679468515326835651547953595104045902497719... are real roots of the system of equations 1 + r*log(1 - r^2*s) = 1/s, r^3*s^2 = 1 - r^2*s. - Vaclav Kotesovec, Aug 31 2024

Mathematica

Table[n!*Sum[(n-k)!*Abs[StirlingS1[k, n - 2*k]]/(k!*(k + 1)!), {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 31 2024 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n-k)!*abs(stirling(k, n-2*k, 1))/(k!*(k+1)!));

Crossrefs

Cf. A371302.

Sequence in context: A375831 A375830 A375833 * A376351 A376350 A376345

Adjacent sequences: A375829 A375830 A375831 * A375833 A375834 A375835

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2024

Status

approved