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 A077261 #39 Aug 15 2024 11:56:05
%S A077261 0,15,105,4950,33930,1594005,10925475,513264780,3517969140,
%T A077261 165269665275,1132775137725,53216318953890,364750076378430,
%U A077261 17135489433487425,117448391818716855,5517574381263997080,37818017415550449000,1776641815277573572455,12177284159415425861265
%N A077261 Triangular numbers that are 5 times another triangular number.
%H A077261 Colin Barker, <a href="/A077261/b077261.txt">Table of n, a(n) for n = 0..797</a>
%H A077261 Vladimir Pletser, <a href="https://arxiv.org/abs/2101.00998">Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers</a>, arXiv:2101.00998 [math.NT], 2021.
%H A077261 Vladimir Pletser, <a href="https://arxiv.org/abs/2102.13494">Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations</a>, arXiv:2102.13494 [math.NT], 2021.
%H A077261 Vladimir Pletser, <a href="https://www.researchgate.net/profile/Vladimir-Pletser/publication/359808848_USING_PELL_EQUATION_SOLUTIONS_TO_FIND_ALL_TRIANGULAR_NUMBERS_MULTIPLE_OF_OTHER_TRIANGULAR_NUMBERS/">Using Pell equation solutions to find all triangular numbers multiple of other triangular numbers</a>, 2022.
%H A077261 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).
%F A077261 a(n) = 5*A077260(n).
%F A077261 G.f.: (-15*x*(x^2+6*x+1))/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%F A077261 a(n) = 322*a(n-2) - a(n-4) + 120. - _Vladimir Pletser_, Feb 09 2021
%F A077261 E.g.f.: (-6*cosh(x) - (-3 + sqrt(5))*cosh((9 - 4*sqrt(5))*x) + (3 + sqrt(5))*cosh((9 + 4*sqrt(5))*x) - 6*sinh(x) + (7 - 3*sqrt(5))*sinh((9 - 4*sqrt(5))*x) + (7 + 3*sqrt(5))*sinh((9 + 4*sqrt(5))*x))/16. - _Stefano Spezia_, Aug 15 2024
%e A077261 a(3)=5*990=4950.
%t A077261 CoefficientList[Series[(-15 x (x^2 + 6 x + 1))/((x - 1) (x^2 - 18 x + 1) (x^2 + 18 x + 1)), {x, 0, 18}], x] (* _Michael De Vlieger_, Apr 21 2021 *)
%Y A077261 Subsequence of A000217.
%Y A077261 Cf. A077259, A077260, A077262.
%K A077261 easy,nonn
%O A077261 0,2
%A A077261 Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002