A238299 Second convolution of A107841.

1, 4, 24, 164, 1208, 9348, 74920, 616420, 5176296, 44182916, 382205048, 3343343268, 29523386968, 262826367748, 2356256046216, 21254326842596, 192766180154120, 1756758963727620, 16079466335134168, 147748236828875428, 1362397741935948024, 12603116216808465284, 116929440001191010664

Offset

0,2

Links

Fung Lam, Table of n, a(n) for n = 0..1000

Formula

G.f.: (G.f. of A107841)^2.

Recurrence: (n+2)*a(n) = (4-n)*a(n-4) + 4*(2*n-5)*a(n-3) + 18*(n-1)*a(n-2) + 4*(2*n+1)*a(n-1), n>=4.

Recurrence (of order 2): (n+2)*(2*n-1)*a(n) = 4*(5*n^2-2)*a(n-1) - (n-2)*(2*n+1)*a(n-2). - Vaclav Kotesovec, Feb 27 2014

a(n) ~ sqrt(360+147*sqrt(6)) * (5+2*sqrt(6))^n / (9 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 27 2014

Mathematica

CoefficientList[Series[((1 + x - Sqrt[1 - 10*x + x^2])/(6*x))^2, {x, 0, 100}], x] (* Vaclav Kotesovec, Feb 27 2014 *)

Crossrefs

Cf. A107841, A238300.

Sequence in context: A343842 A027079 A213441 * A221656 A366623 A339346

Adjacent sequences: A238296 A238297 A238298 * A238300 A238301 A238302

Keyword

nonn,easy

Author

Fung Lam, Feb 25 2014

Status

approved