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 A366014 #7 Feb 16 2025 08:34:06
%S A366014 0,1,6,54,580,6873,86688,1141500,15512220,215928900,3063184410,
%T A366014 44124882750,643692232404,9490176205006,141184118174640,
%U A366014 2116751269990968,31951313566227228,485159929343783532,7405637373574690968,113572576254948487800,1749075343256441443320
%N A366014 G.f. A(x) satisfies: A(x) = x * (1 + A(x))^4 / (1 - 2 * A(x)).
%C A366014 Reversion of g.f. for pentagonal pyramidal numbers (with signs).
%H A366014 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalPyramidalNumber.html">Pentagonal Pyramidal Number</a>
%H A366014 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>
%F A366014 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n+k-1,k) * binomial(4*n,n-k-1) * 2^k for n > 0.
%t A366014 nmax = 20; A[_] = 0; Do[A[x_] = x (1 + A[x])^4/(1 - 2 A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A366014 CoefficientList[InverseSeries[Series[x (1 - 2 x)/(1 + x)^4, {x, 0, 20}], x], x]
%t A366014 Join[{0}, Table[1/n Sum[Binomial[n + k - 1, k] Binomial[4 n, n - k - 1] 2^k, {k, 0, n - 1}], {n, 1, 20}]]
%Y A366014 Cf. A002293, A002411, A064063, A365754, A366015, A366016, A366017.
%K A366014 nonn
%O A366014 0,3
%A A366014 _Ilya Gutkovskiy_, Sep 26 2023