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
KEYWORD
nonn
AUTHOR
STATUS
approved