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.

A337554 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (5*k-4) * a(n-k).

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%I A337554 #9 Sep 01 2020 03:35:13
%S A337554 1,1,8,53,560,6961,105898,1867393,37713620,856269401,21606253238,
%T A337554 599664843433,18156702186880,595557844417441,21037627605306578,
%U A337554 796218790808110673,32143778726932363340,1378765268603813275081,62619174356163136219918,3001963660666272082265113
%N A337554 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (5*k-4) * a(n-k).
%F A337554 E.g.f.: 1 / (exp(x) * (4 - 5*x) - 3).
%F A337554 a(n) ~ n! * c / (3*(1-c) * (4/5 - c)^(n+1)), where c = -LambertW(-3*exp(-4/5)/5). - _Vaclav Kotesovec_, Aug 31 2020
%t A337554 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (5 k - 4) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%t A337554 nmax = 19; CoefficientList[Series[1/(Exp[x] (4 - 5 x) - 3), {x, 0, nmax}], x] Range[0, nmax]!
%o A337554 (PARI) seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (4 - 5*x) - 3)))} \\ _Andrew Howroyd_, Aug 31 2020
%Y A337554 Cf. A000354, A001908, A337552, A337553.
%K A337554 nonn
%O A337554 0,3
%A A337554 _Ilya Gutkovskiy_, Aug 31 2020