A103769 Trinomial transform of central binomial coefficients A001405.

1, 4, 21, 123, 757, 4788, 30817, 200784, 1320093, 8740284, 58193673, 389233287, 2613338091, 17602627006, 118892784555, 804951501469, 5461228061541, 37120212399708, 252720891884473, 1723088114793535, 11763751150648785

Offset

0,2

Links

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

Formula

a(n) = sum_{k=0..2n} T(n,k)*C(k,floor(k/2)), where T(n,k) is given by A027907.

a(n) = sum_{k=0..n} sum_{j=0..n} C(n,j)*C(j,k)*C(j+k,floor((j+k)/2)).

G.f.: ((3*x+1-(21*x^2-10*x+1)^(1/2))/(2*x*(3*x-4)*(7*x-1)))^(1/2). - Mark van Hoeij, Nov 16 2011

Conjecture: n*(2n+1)*a(n) +2(-61n^2+57n-20)*a(n-1) +3*(205n^2-523*n+346) * a(n-2) -72*(n-2)*(16n-33)*a(n-3) +567*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Dec 14 2011

a(n) ~ 7^(n+1/2)/sqrt(5*Pi*n). - Vaclav Kotesovec, Oct 24 2012

Mathematica

CoefficientList[Series[((3*x+1-(21*x^2-10*x+1)^(1/2))/(2*x*(3*x-4)*(7*x-1)))^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)

Crossrefs

Cf. A082760.

Sequence in context: A236525 A277292 A001888 * A003014 A108404 A115136

Adjacent sequences: A103766 A103767 A103768 * A103770 A103771 A103772

Keyword

easy,nonn

Author

Paul Barry, Feb 15 2005

Status

approved