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.

A337552 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (3*k-2) * a(n-k).

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%I A337552 #9 Aug 31 2020 19:18:20
%S A337552 1,1,6,37,330,3613,47652,732625,12875118,254540413,5591435136,
%T A337552 135108218353,3561467337546,101704047315037,3127751183515020,
%U A337552 103059820083026449,3622223857996975110,135266462416766669917,5348457650664454581240,223227700948792985989777
%N A337552 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (3*k-2) * a(n-k).
%F A337552 E.g.f.: 1 / (exp(x) * (2 - 3*x) - 1).
%F A337552 a(n) ~ n! * c / ((1-c) * (2/3 - c)^(n+1)), where c = -LambertW(-exp(-2/3)/3). - _Vaclav Kotesovec_, Aug 31 2020
%t A337552 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (3 k - 2) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%t A337552 nmax = 19; CoefficientList[Series[1/(Exp[x] (2 - 3 x) - 1), {x, 0, nmax}], x] Range[0, nmax]!
%o A337552 (PARI) seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (2 - 3*x) - 1)))} \\ _Andrew Howroyd_, Aug 31 2020
%Y A337552 Cf. A000180, A000354, A337553, A337554.
%K A337552 nonn
%O A337552 0,3
%A A337552 _Ilya Gutkovskiy_, Aug 31 2020