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.

A076012 Sixth column of triangle A075504.

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%I A076012 #10 Dec 25 2017 04:01:52
%S A076012 1,189,21546,1928934,149767947,10598527863,703442942532,
%T A076012 44583546335328,2730727849782933,162985193544670497,
%U A076012 9536099260315021758,549348981049383669882,31261349005300855653759
%N A076012 Sixth column of triangle A075504.
%C A076012 The e.g.f. given below is Sum_{m=0..5} (A075513(6,m)*exp(9*(m+1)*x))/5!.
%H A076012 Michael De Vlieger, <a href="/A076012/b076012.txt">Table of n, a(n) for n = 0..576</a>
%F A076012 a(n) = A075504(n+6, 6) = (9^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).
%F A076012 a(n) = Sum_{m=0..5} (A075513(6, m)*((m+1)*9)^n)/5!.
%F A076012 G.f.: 1/Product_{k=1..6} (1 - 9*k*x).
%F A076012 E.g.f.: (d^6/dx^6)(((exp(9*x)-1)/9)^6)/6! = (-exp(9*x) + 160*exp(18*x) - 2430*exp(27*x) + 10240*exp(36*x) - 15625*exp(45*x) + 7776*exp(54*x))/5!.
%t A076012 With[{m = 6}, Array[9^(# - m) StirlingS2[#, m] &, 13, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075504 *)
%Y A076012 Cf. A076011, A076013.
%K A076012 nonn,easy
%O A076012 0,2
%A A076012 _Wolfdieter Lang_, Oct 02 2002