This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117152 #8 May 16 2025 07:27:54
%S A117152 0,0,1,7,25,75,195,468,1056,2280,4755,9650,19154,37328,71635,135685,
%T A117152 254125,471317,866669,1581620,2866970,5165630,9256871,16507092,
%U A117152 29304660,51812160,91264885,160207603,280340161,489117135,851054535
%N A117152 Sum of product of Fibonacci and triangular numbers.
%D A117152 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003
%F A117152 a(n) = Sum_{k=2..n} C(k,2)*F(k), where F(n) = A000045(n), the Fibonacci numbers and C(n, 2) = A000217(n-1), the triangular numbers, n(n-1)/2.
%F A117152 a(n) = C(n,2) F(n+2) - n F(n+3) + F(n+5) - 5.
%F A117152 G.f.: x^2(1 + 3x + x^3)/((1 - x)(1 - x - x^2)^3).
%F A117152 a(n)-a(n-1) = A086926(n). - _R. J. Mathar_, May 16 2025
%t A117152 Binomial[n, 2]Fibonacci[n + 2] - n Fibonacci[n + 3] + Fibonacci[n + 5] - 5
%o A117152 (PARI) a(n) = sum(k=2, n, k*(k-1)*fibonacci(k)/2); \\ _Michel Marcus_, Feb 28 2019
%Y A117152 Cf. A086926, A014286.
%K A117152 nonn,easy
%O A117152 0,4
%A A117152 _Mitch Harris_, Feb 28 2006