A026020 a(n) = binomial(4n, n) - binomial(4n, n - 3).

1, 4, 28, 219, 1804, 15314, 132572, 1163565, 10316924, 92195488, 829016968, 7492106505, 67991427828, 619193535380, 5655829748520, 51794730347745, 475390078267356, 4371917301657488, 40276635724273936

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

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

Bisections are A026012 and A026016.

Cf. A004333, A005810.

Programs

Magma

[Binomial(4*n, n) - Binomial(4*n, n-3): n in [0..20]]; // G. C. Greubel, Mar 22 2021

Maple

A026020:= n-> binomial(4*n,n) - binomial(4*n,n-3); seq(A026020(n), n=0..20); # G. C. Greubel, Mar 22 2021

Mathematica

Table[Binomial[4n, n] - Binomial[4n, n - 3], {n, 0, 19}] (* Alonso del Arte, Jun 06 2019 *)

PARI

a(n) = binomial(4*n, n) - binomial(4*n, n-3) \\ Felix Fröhlich, Jun 06 2019

Sage

[binomial(4*n, n) - binomial(4*n, n-3) for n in (0..20)] # G. C. Greubel, Mar 22 2021

Formula

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

a(n) = A005810(n) - A004333(n) for n > 2 - Felix Fröhlich, Jun 06 2019