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A103769
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Trinomial transform of central binomial coefficients A001405.
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0
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1, 4, 21, 123, 757, 4788, 30817, 200784, 1320093, 8740284, 58193673, 389233287, 2613338091, 17602627006, 118892784555, 804951501469, 5461228061541, 37120212399708, 252720891884473, 1723088114793535, 11763751150648785
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=sum{k=0..2n, T(n, k)*binomial(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
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CROSSREFS
| Cf. A082760.
Sequence in context: A045721 A101810 A001888 * A003014 A108404 A115136
Adjacent sequences: A103766 A103767 A103768 * A103770 A103771 A103772
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 15 2005
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