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A238473 a(n) = binomial(5*n+8, 4)/5 for n >= 0. 2
14, 143, 612, 1771, 4095, 8184, 14763, 24682, 38916, 58565, 84854, 119133, 162877, 217686, 285285, 367524, 466378, 583947, 722456, 884255, 1071819, 1287748, 1534767, 1815726, 2133600, 2491489, 2892618, 3340337, 3838121, 4389570, 4998409, 5668488, 6403782, 7208391 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
This sequence appears in the 5-section of A234042.
LINKS
FORMULA
a(n) = binomial(5*n+8, 4)/5 = (5*n+8)*(5*n+7)*(5*n+6)*(n+1)/4! for n >= 0.
a(n) = A234042(5*n+2) for n >= 0.
a(n) = 14*b(n) + 73*b(n-1) + 37*b(n-2) + b(n-3), with b(n) = binomial(n+4,4) = A000332(n) for n >= 0.
O.g.f.: (14 + 73*x + 37*x^2 + x^3)/(1-x)^5.
Sum_{n>=0} 1/a(n) = 110/3 - 2*sqrt(25 - 38/sqrt(5))*Pi - 10*sqrt(5)*log(phi) - 5*log(5), where phi is the golden ratio (A001622). - Amiram Eldar, Sep 20 2022
MATHEMATICA
a[n_] := Binomial[5*n + 8, 4]/5; Array[a, 40, 0] (* Amiram Eldar, Sep 20 2022 *)
CROSSREFS
Sequence in context: A241217 A159500 A167834 * A016233 A276250 A099914
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 28 2014
STATUS
approved

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Last modified March 2 21:08 EST 2024. Contains 370498 sequences. (Running on oeis4.)