A027390 Number of labeled servers of dimension 3.

1, 3, 12, 56, 294, 1698, 10624, 71256, 508188, 3829652, 30340464, 251647872, 2177440648, 19596586584, 182967013056, 1768251873632, 17653554391056, 181748836240944, 1926542292294592, 20996051677557888, 234959167687868256, 2696726674789023008

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

R. Donaghey, Binomial self-inverse sequences and tangent coefficients, J. Combin. Theory, Series A, 21 (1976), 155-163.

Formula

E.g.f.: exp( (x*(18 + 9*x + 2*x^2))/6 ).

a(n) = 3*a(n-1) + 3*(n-1)*a(n-2) + (n-1)*(n-2)*a(n-3). - Vaclav Kotesovec, Dec 29 2012 [unless n=0, Michael Somos, May 31 2014]

a(n) ~ exp(3/2*n^(1/3)+3/2*n^(2/3)-2*n/3-3/2)*n^(2*n/3)/sqrt(3) * (1 + 3/(4*n^(1/3)) + 117/(160*n^(2/3)) - 59/(640*n)). - Vaclav Kotesovec, Dec 29 2012

Example

G.f. = 1 + 3*x + 12*x^2 + 56*x^3 + 294*x^4 + 1698*x^5 + 10624*x^6 + ...

Mathematica

Table[n!*SeriesCoefficient[E^((x*(18 + 9*x + 2*x^2))/6), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 29 2012 *)

Prog

(Magma) I:=[1, 3, 12, 56]; [n le 3 select I[n] else 3*Self(n-1)+3*(n-2)*Self(n-2)+(n^2 -5*n+6)*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Dec 31 2012
(PARI) {a(n) = if( n<0, 0, n! * polcoeff( exp((18*x + 9*x^2 + 2*x^3) / 6 + x * O(x^n)), n))}; /* Michael Somos, May 31 2014 */
(PARI) {a(n) = if( n<1, n==0, 3 * a(n-1) + 3*(n-1) * a(n-2) + (n-1)*(n-2) * a(n-3))}; /* Michael Somos, May 31 2014 */

Crossrefs

Sequence in context: A284713 A180256 A369600 * A349513 A009499 A009656

Adjacent sequences: A027387 A027388 A027389 * A027391 A027392 A027393

Keyword

nonn

Author

Olivier Gérard

Status

approved