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 A213837 #23 Aug 07 2025 15:30:16
%S A213837 1,13,52,134,275,491,798,1212,1749,2425,3256,4258,5447,6839,8450,
%T A213837 10296,12393,14757,17404,20350,23611,27203,31142,35444,40125,45201,
%U A213837 50688,56602,62959,69775,77066,84848,93137
%N A213837 Principal diagonal of the convolution array A213836.
%H A213837 Clark Kimberling, <a href="/A213837/b213837.txt">Table of n, a(n) for n = 1..1000</a>
%H A213837 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A213837 a(n) = n*(5 - 15*n + 16*n^2)/6.
%F A213837 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A213837 G.f.: f(x)/g(x), where f(x) = x*(1 + 9*x + 6*x^2) and g(x) = (1-x)^4.
%F A213837 a(n) = n*A002412(n) - (n-1)*A002412(n-1). [_Bruno Berselli_, Dec 11 2012]
%F A213837 a(n) = n*A000384(n) + sum( A000384(i), i=0..n-1 ). [_Bruno Berselli_, Dec 18 2013]
%t A213837 (See A213836.)
%t A213837 LinearRecurrence[{4,-6,4,-1},{1,13,52,134},40] (* _Harvey P. Dale_, Aug 07 2025 *)
%Y A213837 Cf. A000384, A002412, A213836, A220084 (for a list of numbers of the form n*P(k,n)-(n-1)*P(k,n-1), where P(k,n) is the n-th k-gonal pyramidal number).
%K A213837 nonn,easy
%O A213837 1,2
%A A213837 _Clark Kimberling_, Jul 04 2012