A238755 Second convolution of A065096.

0, 0, 1, 12, 98, 684, 4403, 27048, 161412, 945288, 5466549, 31340628, 178604998, 1013573652, 5735117479, 32385232272, 182622362504, 1028897389008, 5793703249449, 32615362319580, 183593293074730, 1033535639454780, 5819389057957211, 32775522041862072, 184658694508103180

Offset

0,4

Links

Fung Lam, Table of n, a(n) for n = 0..1300

Formula

G.f. = (G.f. of A065096)^2.

Recurrence: (n+6)*a(n) = 225*(6-n)*a(n-8) + 1020*(2*n-9)*a(n-7) + 5164*(3-n)*a(n-6) + 76*(78*n-117)*a(n-5) - 3590*n*a(n-4) + 36*(34*n+51)*a(n-3) - 236*(n+3)*a(n-2) + 12*(2*n+9)*a(n-1), n>=8.

Recurrence (of order 2): (n-2)*(n+6)*a(n) = 3*(n+1)*(2*n+3)*a(n-1) - n*(n+1)*a(n-2). - Vaclav Kotesovec, Mar 05 2014

a(n) ~ (3*sqrt(2)-4)^(7/2) * (3+2*sqrt(2))^(n+6) / (8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 05 2014

Mathematica

CoefficientList[Series[(1-3*x-Sqrt[1-6*x+x^2])^4/(16*x^3)^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 05 2014 *)

Prog

(PARI) x='x+O('x^50); concat([0, 0], Vec((1-3*x-sqrt(1-6*x+x^2))^4/(16*x^3)^2)) \\ G. C. Greubel, Apr 05 2017

Crossrefs

Cf. A065096, A000108, A001003.

Sequence in context: A041268 A216028 A378728 * A159449 A373412 A282285

Adjacent sequences: A238752 A238753 A238754 * A238756 A238757 A238758

Keyword

nonn,easy

Author

Fung Lam, Mar 04 2014

Status

approved