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.

A076009 Third column of triangle A075504.

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%I A076009 #10 Dec 25 2017 04:01:41
%S A076009 1,54,2025,65610,1974861,57041334,1607609025,44625100770,
%T A076009 1226874595221,33521945231214,912229968911625,24758714599712730,
%U A076009 670798674525559581,18153207600055622694,490886209059873519825
%N A076009 Third column of triangle A075504.
%C A076009 The e.g.f. given below is Sum_{m=0..2} (A075513(3,m)*exp(9*(m+1)*x))/2!.
%H A076009 Michael De Vlieger, <a href="/A076009/b076009.txt">Table of n, a(n) for n = 0..698</a>
%F A076009 a(n) = A075504(n+3, 3) = (9^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).
%F A076009 a(n) = (9^n - 8*18^n + 9*27^n)/2.
%F A076009 G.f.: 1/Product_{k=1..3} (1 - 9*k*x).
%F A076009 E.g.f.: (d^3/dx^3)(((exp(9*x)-1)/9)^3)/3! = (exp(9*x) - 8*exp(18*x) + 9*exp(27*x))/2!.
%t A076009 With[{m = 3}, Array[9^(# - m) StirlingS2[#, m] &, 15, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075504 *)
%Y A076009 Cf. A076008, A076010.
%K A076009 nonn,easy
%O A076009 0,2
%A A076009 _Wolfdieter Lang_, Oct 02 2002