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 A071238 #67 Feb 16 2024 05:49:06
%S A071238 0,1,9,38,110,255,511,924,1548,2445,3685,5346,7514,10283,13755,18040,
%T A071238 23256,29529,36993,45790,56070,67991,81719,97428,115300,135525,158301,
%U A071238 183834,212338,244035,279155,317936,360624,407473,458745,514710,575646,641839
%N A071238 a(n) = n*(n+1)*(2*n^2+1)/6.
%C A071238 Binomial transform of [1, 8, 21, 22, 8, 0, 0, 0, ...]. - _Gary W. Adamson_, Dec 28 2007
%C A071238 For n > 0, a(n) is the n-th antidiagonal sum of the convolution arrays A213752 and A213836). - _Clark Kimberling_, Jun 20 2012
%C A071238 The first differences are given in A277229, as a convolution of the odd-indexed triangular numbers A000217(2*n+1) and the squares A000290(n), n >= 0. - _J. M. Bergot_, Sep 14 2016
%D A071238 T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H A071238 Vincenzo Librandi, <a href="/A071238/b071238.txt">Table of n, a(n) for n = 0..2000</a>
%H A071238 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A071238 G.f.: x*(1+x)*(1+3*x)/(1-x)^5. - _Colin Barker_, Mar 22 2012
%F A071238 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4, a(0)=0, a(1)=1, a(2)=9, a(3)=38, a(4)=110. - _Yosu Yurramendi_, Sep 03 2013
%F A071238 E.g.f.: (1/6)*x*(6 + 21*x + 14*x^2 + 2*x^3)*exp(x). - _G. C. Greubel_, Sep 17 2016
%F A071238 a(n) = n*A000292(n) + (n-1)*A000292(n-1). - _Bruno Berselli_, Sep 22 2016
%F A071238 a(n) = A002417(n-1) + A002417(n). - _Yasser Arath Chavez Reyes_, Feb 15 2024
%p A071238 A071238:=n->n*(n+1)*(2*n^2+1)/6: seq(A071238(n), n=0..60); # _Wesley Ivan Hurt_, Sep 24 2016
%t A071238 Table[n (n + 1) (2 n^2 + 1)/6, {n, 0, 37}] (* or *)
%t A071238 CoefficientList[Series[x (1 + x) (1 + 3 x)/(1 - x)^5, {x, 0, 37}], x] (* _Michael De Vlieger_, Sep 14 2016 *)
%t A071238 LinearRecurrence[{5,-10,10,-5,1},{0,1,9,38,110},40] (* _Harvey P. Dale_, Oct 02 2021 *)
%o A071238 (Magma) [n*(n+1)*(2*n^2+1)/6: n in [0..40]]; // _Vincenzo Librandi_, Jun 14 2011
%o A071238 (PARI) a(n)=n*(n+1)*(2*n^2+1)/6; \\ _Joerg Arndt_, Sep 04 2013
%Y A071238 Cf. A000292, A002417, A071270, A277229 (first differences).
%K A071238 nonn,easy
%O A071238 0,3
%A A071238 _N. J. A. Sloane_, Jun 12 2002