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 A329755 #8 Feb 16 2025 08:33:58
%S A329755 0,1,252,7337,84575,576080,2795121,10700382,34388362,96606475,
%T A329755 243939410,564840991,1217275137,2469392562,4757404575,8765621740,
%U A329755 15534503236,26603512517,44196596312,71459197125,112756874195,174046844356,263335062397,391232840362,571628456750,822490729775
%N A329755 Doubly hexagonal pyramidal numbers.
%H A329755 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalPyramidalNumber.html">Hexagonal Pyramidal Number</a>
%H A329755 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H A329755 <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 A329755 G.f.: x*(1 + 242*x + 4862*x^2 + 22425*x^3 + 30465*x^4 + 12424*x^5 + 1248*x^6 + 13*x^7)/(1 - x)^10.
%F A329755 a(n) = A002412(A002412(n)).
%F A329755 a(n) = Sum_{k=0..A002412(n)} A000384(k).
%F A329755 a(n) = n *(4*n-1) *(n+1) *(4*n^3+3*n^2-n+6) *(8*n^3+6*n^2-2*n-3) / 648 . - _R. J. Mathar_, Nov 28 2019
%t A329755 A002412[n_] := n (n + 1) (4 n - 1)/6; a[n_] := A002412[A002412[n]]; Table[a[n], {n, 0, 25}]
%t A329755 Table[Sum[k (2 k - 1), {k, 0, n (n + 1) (4 n - 1)/6}], {n, 0, 25}]
%t A329755 nmax = 25; CoefficientList[Series[x (1 + 242 x + 4862 x^2 + 22425 x^3 + 30465 x^4 + 12424 x^5 + 1248 x^6 + 13 x^7)/(1 - x)^10, {x, 0, nmax}], x]
%t A329755 LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 252, 7337, 84575, 576080, 2795121, 10700382, 34388362, 96606475}, 26]
%Y A329755 Cf. A000384, A002412, A063249, A140236, A329753, A329754, A329756, A329757.
%K A329755 nonn,easy
%O A329755 0,3
%A A329755 _Ilya Gutkovskiy_, Nov 20 2019