A238471 a(n) = binomial(5n+6, 4)/5 for n >= 0.

3, 66, 364, 1197, 2990, 6293, 11781, 20254, 32637, 49980, 73458, 104371, 144144, 194327, 256595, 332748, 424711, 534534, 664392, 816585, 993538, 1197801, 1432049, 1699082, 2001825, 2343328, 2726766, 3155439, 3632772, 4162315, 4747743, 5392856, 6101579, 6877962

Offset: 0

Author

Wolfdieter Lang, Feb 28 2014

Keywords

• nonn
• easy

Comments

This sequence appears in the 5-section of A234042.

Crossrefs

Cf. A000332, A001622, A234042, A151989, A234043, A238472, A238473.

Programs

Mathematica

a[n_] := Binomial[5*n + 6, 4]/5; Array[a, 40, 0] (* Amiram Eldar, Sep 20 2022 *)

Formula

a(n) = binomial(5*n+6, 4)/5 = (5*n+6)*(5*n+3)*(5*n+4)*(n+1)/4! for n >= 0.

a(n) = A234042(5*n+2) for n >= 0.

a(n) = 3*b(n) + 51*b(n-1) + 64*b(n-2) + 7*b(n-3), with b(n) = binomial(n+4,4) = A000332(n) for n >= 0.

O.g.f.: (3 + 51*x + 64*x^2 + 7*x^3)/(1-x)^5.

Sum_{n>=0} 1/a(n) = 2*sqrt(5+2/sqrt(5))*Pi - 10*sqrt(5)*log(phi) - 15*log(5) + 20, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 20 2022