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A238471
a(n) = binomial(5n+6, 4)/5 for n >= 0.
2
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
0,1
COMMENTS
This sequence appears in the 5-section of A234042.
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
MATHEMATICA
a[n_] := Binomial[5*n + 6, 4]/5; Array[a, 40, 0] (* Amiram Eldar, Sep 20 2022 *)
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 28 2014
STATUS
approved