%I #14 Sep 20 2022 02:38:00
%S 7,99,476,1463,3510,7192,13209,22386,35673,54145,79002,111569,153296,
%T 205758,270655,349812,445179,558831,692968,849915,1032122,1242164,
%U 1482741,1756678,2066925,2416557,2808774,3246901,3734388,4274810,4871867,5529384,6251311,7041723
%N a(n) = binomial(5*n+7, 4)/5 for n >= 0.
%C This sequence appears in the 5-section of A234042.
%F a(n) = binomial(5*n+7, 4)/5 for n >= 0.
%F a(n) = A234042(5*n+3) for n >= 0.
%F 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.
%F O.g.f.: (7 + 64*x + 51*x^2 + 3*x^3)/(1-x)^5.
%F 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
%t a[n_] := Binomial[5*n + 7, 4]/5; Array[a, 40, 0] (* _Amiram Eldar_, Sep 20 2022 *)
%Y Cf. A000332, A001622, A234042, A151989, A234043, A238471, A238473.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Feb 28 2014
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