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.

A179431 a(n) = binomial(3^(n-1), n).

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%I A179431 #8 Apr 13 2021 18:58:56
%S A179431 1,1,3,84,17550,25621596,268715232324,21091830512086620,
%T A179431 12814543323816738705045,61742372998425082372103866380,
%U A179431 2399699340005498870742886195375900380,761689137813999393167583510790986701377432464,1992997938492157367948224731863936229108552184201415196
%N A179431 a(n) = binomial(3^(n-1), n).
%C A179431 Equals column 0 of triangle T=A179430 where column 0 of T^m equals C(m*3^(n-1), n) at row n for n>=0, m>=0.
%H A179431 Andrew Howroyd, <a href="/A179431/b179431.txt">Table of n, a(n) for n = 0..40</a>
%F A179431 G.f.: A(x) = Sum_{n>=0} (1/3)^n * log(1 + 3^n*x)^n / n!.
%F A179431 a(n) ~ 3^(n*(n-1)) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%e A179431 G.f.: A(x) = 1 + x + 3*x^2 + 84*x^3 + 17550*x^4 + 25621596*x^5 +...
%e A179431 A(x) = 1 + log(1+3*x)/3 + log(1+3^2*x)^2/(3^2*2!) + log(1+3^3*x)^3/(3^3*3!) + log(1+3^4*x)^4/(3^4*4!) +...
%t A179431 Table[Binomial[3^(n-1),n], {n,0,15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)
%o A179431 (PARI) a(n)=binomial(3^(n-1), n)
%o A179431 (PARI) /* G.f. A(x) as Sum of Series: */
%o A179431 {a(n)=polcoeff(sum(k=0, n, (1/3)^k*log(1+3^k*x +x*O(x^n))^k/k!), n)}
%Y A179431 Cf. A179430, A179432, A136393, A179433, A179434.
%K A179431 nonn
%O A179431 0,3
%A A179431 _Paul D. Hanna_, Jul 20 2010
%E A179431 Terms a(11) and beyond from _Andrew Howroyd_, Apr 13 2021