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 A329753 #8 Feb 16 2025 08:33:58
%S A329753 0,1,55,1015,9455,56980,255346,924490,2850730,7757035,19096385,
%T A329753 43312841,91753025,183453270,349074740,636310340,1117143236,
%U A329753 1897397285,3129084635,5026125195,7884086595,12104671656,18225763270,26957923950,39228339150,56233289775,79500340101,110961532605
%N A329753 Doubly square pyramidal numbers.
%H A329753 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePyramidalNumber.html">Square Pyramidal Number</a>
%H A329753 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H A329753 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A329753 G.f.: x*(1 + 45*x + 510*x^2 + 1660*x^3 + 1715*x^4 + 519*x^5 + 30*x^6)/(1 - x)^10.
%F A329753 a(n) = A000330(A000330(n)).
%F A329753 a(n) = Sum_{k=0..A000330(n)} A000290(k).
%F A329753 a(n) = n *(2*n+1) *(n+2) *(n+1) *(2*n^2-n+3) *(2*n^3+3*n^2+n+3) /648. - _R. J. Mathar_, Nov 28 2019
%t A329753 A000330[n_] := n (n + 1) (2 n + 1)/6; a[n_] := A000330[A000330[n]]; Table[a[n], {n, 0, 27}]
%t A329753 Table[Sum[k^2, {k, 0, n (n + 1) (2 n + 1)/6}], {n, 0, 27}]
%t A329753 nmax = 27; CoefficientList[Series[x (1 + 45 x + 510 x^2 + 1660 x^3 + 1715 x^4 + 519 x^5 + 30 x^6)/(1 - x)^10, {x, 0, nmax}], x]
%t A329753 LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 55, 1015, 9455, 56980, 255346, 924490, 2850730, 7757035}, 28]
%Y A329753 Cf. A000290, A000330, A000583, A140236, A329754, A329755, A329756, A329757.
%K A329753 nonn,easy
%O A329753 0,3
%A A329753 _Ilya Gutkovskiy_, Nov 20 2019