A238471 - OEIS

%I #15 Sep 20 2022 02:08:05

%S 3,66,364,1197,2990,6293,11781,20254,32637,49980,73458,104371,144144,

%T 194327,256595,332748,424711,534534,664392,816585,993538,1197801,

%U 1432049,1699082,2001825,2343328,2726766,3155439,3632772,4162315,4747743,5392856,6101579,6877962

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

%C This sequence appears in the 5-section of A234042.

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

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

%F 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.

%F O.g.f.: (3 + 51*x + 64*x^2 + 7*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) + 20, where phi is the golden ratio (A001622). - _Amiram Eldar_, Sep 20 2022

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

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

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Feb 28 2014