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.

A053116 a(n) = ((9*n+10)(!^9))/10, related to A045756 ((9*n+1)(!^9) 9-factorials).

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%I A053116 #16 Sep 08 2022 08:45:00
%S A053116 1,19,532,19684,905464,49800520,3187233280,232668029440,
%T A053116 19078778414080,1736168835681280,173616883568128000,
%U A053116 18924240308925952000,2233060356453262336000,283598665269564316672000
%N A053116 a(n) = ((9*n+10)(!^9))/10, related to A045756 ((9*n+1)(!^9) 9-factorials).
%C A053116 Row m=10 of the array A(10; m,n) := ((9*n+m)(!^9))/m(!^9), m >= 0, n >= 0.
%H A053116 G. C. Greubel, <a href="/A053116/b053116.txt">Table of n, a(n) for n = 0..327</a>
%F A053116 a(n) = ((9*n+10)(!^9))/10(!^9) = A045756(n+2)/10.
%F A053116 E.g.f.: 1/(1-9*x)^(19/9).
%t A053116 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 18, 3*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t A053116 With[{nmax = 50}, CoefficientList[Series[1/(1 - 9*x)^(19/9), {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Aug 26 2018 *)
%o A053116 (PARI) x='x+O('x^25); Vec(serlaplace(1/(1 - 9*x)^(19/9))) \\ _G. C. Greubel_, Aug 26 2018
%o A053116 (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/(1 - 9*x)^(19/9))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 26 2018
%Y A053116 Cf. A051232, A045756, A035012-3, A035017-8, A035020-3 (rows m=0..9).
%K A053116 easy,nonn
%O A053116 0,2
%A A053116 _Wolfdieter Lang_