cp's OEIS Frontend

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.

A025760 7th-order Vatalan numbers (generalization of Catalan numbers).

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%I A025760 #15 Aug 04 2024 12:43:34
%S A025760 1,1,22,680,24074,917414,36618492,1508943612,63643109727,
%T A025760 2732349490669,118957846271104,5237911268468572,232794783971436296,
%U A025760 10427673857731312064,470213556090357498728,21325335129901497816528
%N A025760 7th-order Vatalan numbers (generalization of Catalan numbers).
%H A025760 Vincenzo Librandi, <a href="/A025760/b025760.txt">Table of n, a(n) for n = 0..200</a>
%F A025760 G.f.: 7/(6 + (1 - 49*x)^(1/7)).
%F A025760 a(n) = (-1)^(n+1) * 7^(2*n+1) * Sum_{k>=0} (-1/6)^(k+1) * binomial(k/7,n). - _Seiichi Manyama_, Aug 04 2024
%t A025760 Table[SeriesCoefficient[7/(6 + (1 - 49*x)^(1/7)), {x, 0, n}], {n, 0, 20}] (* _Vincenzo Librandi_, Dec 29 2012 *)
%Y A025760 Cf. A000108, A025756, A025757, A025758, A025759, A025761, A025762, A025763.
%K A025760 nonn
%O A025760 0,3
%A A025760 _Olivier Gérard_