

A103769


Trinomial transform of central binomial coefficients A001405.


1



1, 4, 21, 123, 757, 4788, 30817, 200784, 1320093, 8740284, 58193673, 389233287, 2613338091, 17602627006, 118892784555, 804951501469, 5461228061541, 37120212399708, 252720891884473, 1723088114793535, 11763751150648785
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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^210*x+1)^(1/2))/(2*x*(3*x4)*(7*x1)))^(1/2).  Mark van Hoeij, Nov 16 2011
Conjecture: n*(2n+1)*a(n) +2(61n^2+57n20)*a(n1) +3*(205n^2523*n+346) * a(n2) 72*(n2)*(16n33)*a(n3) +567*(n2)*(n3)*a(n4)=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^210*x+1)^(1/2))/(2*x*(3*x4)*(7*x1)))^(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



