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a(n) = binomial(4n, n) - binomial(4n, n - 3).
2

%I #26 Mar 23 2021 02:52:33

%S 1,4,28,219,1804,15314,132572,1163565,10316924,92195488,829016968,

%T 7492106505,67991427828,619193535380,5655829748520,51794730347745,

%U 475390078267356,4371917301657488,40276635724273936

%N a(n) = binomial(4n, n) - binomial(4n, n - 3).

%H G. C. Greubel, <a href="/A026020/b026020.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (g - 2)*(1 - g + g^2)*g/(3*g - 4) where g = 1 + x*g^4 is the g.f. of A002293. - _Mark van Hoeij_, Nov 11 2011

%F a(n) = A005810(n) - A004333(n) for n > 2 - _Felix Fröhlich_, Jun 06 2019

%p A026020:= n-> binomial(4*n,n) - binomial(4*n,n-3); seq(A026020(n), n=0..20); # _G. C. Greubel_, Mar 22 2021

%t Table[Binomial[4n, n] - Binomial[4n, n - 3], {n, 0, 19}] (* _Alonso del Arte_, Jun 06 2019 *)

%o (PARI) a(n) = binomial(4*n, n) - binomial(4*n, n-3) \\ _Felix Fröhlich_, Jun 06 2019

%o (Magma) [Binomial(4*n, n) - Binomial(4*n, n-3): n in [0..20]]; // _G. C. Greubel_, Mar 22 2021

%o (Sage) [binomial(4*n, n) - binomial(4*n, n-3) for n in (0..20)] # _G. C. Greubel_, Mar 22 2021

%Y a(n) = T(4n, n), where T is the array defined in A026009.

%Y Bisections are A026012 and A026016.

%Y Cf. A004333, A005810.

%K nonn

%O 0,2

%A _Clark Kimberling_