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A238472
a(n) = binomial(5*n+7, 4)/5 for n >= 0.
2
7, 99, 476, 1463, 3510, 7192, 13209, 22386, 35673, 54145, 79002, 111569, 153296, 205758, 270655, 349812, 445179, 558831, 692968, 849915, 1032122, 1242164, 1482741, 1756678, 2066925, 2416557, 2808774, 3246901, 3734388, 4274810, 4871867, 5529384, 6251311, 7041723
OFFSET
0,1
COMMENTS
This sequence appears in the 5-section of A234042.
FORMULA
a(n) = binomial(5*n+7, 4)/5 for n >= 0.
a(n) = A234042(5*n+3) for n >= 0.
a(n) = 7*b(n) + 64*b(n-1) + 51*b(n-2) + 3*b(n-3), with b(n) = binomial(n+4,4) = A000332(n) for n >= 0.
O.g.f.: (7 + 64*x + 51*x^2 + 3*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) - 50, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 20 2022
MATHEMATICA
a[n_] := Binomial[5*n + 7, 4]/5; Array[a, 40, 0] (* Amiram Eldar, Sep 20 2022 *)
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 28 2014
STATUS
approved