A055218 a(n) = T(2*n+2,n), array T as in A055216.

1, 4, 15, 51, 168, 540, 1711, 5365, 16698, 51679, 159250, 489048, 1497681, 4576140, 13955895, 42493677, 129211818, 392441049, 1190716836, 3609608838, 10933915743, 33097421223, 100126350090, 302737691646, 914897836063

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: ((2*x-1) *sqrt(-3*x^2-2*x+1)+2*x^3-3*x+1)/ (6*x^6+x^5 +sqrt(-3*x^2-2*x+1) *(3*x^4-x^3)-4*x^4+x^3). - Vladimir Kruchinin, May 24 2014

a(n) ~ 3^(n+2)/2 * (1-3*sqrt(3)/(2*sqrt(Pi*n))). - Vaclav Kotesovec, May 24 2014

Mathematica

Table[Sum[Binomial[n+2, i]*Sum[Binomial[i, j], {j, 0, n-i}], {i, 0, n+2}], {n, 0, 20}] (* Vaclav Kotesovec, May 24 2014 *)

Prog

(PARI) x='x+O('x^50); Vec(((2*x-1)*sqrt(-3*x^2-2*x+1)+2*x^3-3*x+ 1)/(6*x^6 +x^5 + sqrt(-3*x^2-2*x+1)*(3*x^4-x^3)-4*x^4+x^3)) \\ G. C. Greubel, May 23 2017

Crossrefs

Cf. A055216.

Sequence in context: A280786 A283276 A196835 * A303843 A107307 A240365

Adjacent sequences: A055215 A055216 A055217 * A055219 A055220 A055221

Keyword

nonn

Author

Clark Kimberling, May 07 2000

Status

approved