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.

A076010 Fourth column of triangle A075504.

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%I A076010 #10 Dec 25 2017 04:01:45
%S A076010 1,90,5265,255150,11160261,458810730,18124795305,697117731750,
%T A076010 26323112938221,981154011007170,36233774365169745,1329174591745823550,
%U A076010 48521083977375207381,1764912230785563088410,64027726517340144702585
%N A076010 Fourth column of triangle A075504.
%C A076010 The e.g.f. given below is Sum_{m=0..3} (A075513(4,m)*exp(9*(m+1)*x))/3!.
%H A076010 Michael De Vlieger, <a href="/A076010/b076010.txt">Table of n, a(n) for n = 0..641</a>
%F A076010 a(n) = A075504(n+4, 4) = (9^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).
%F A076010 a(n) = (-9^n + 24*18^n - 81*27^n + 64*36^n)/3!.
%F A076010 G.f.: 1/Product_{k=1..4} (1 - 9*k*x).
%F A076010 E.g.f.: (d^4/dx^4)(((exp(9*x)-1)/9)^4)/4! = (-exp(9*x) + 24*exp(18*x) - 81*exp(27*x) + 64*exp(36*x))/3!.
%t A076010 With[{m = 4}, Array[9^(# - m) StirlingS2[#, m] &, 15, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075504 *)
%Y A076010 Cf. A076009, A076011.
%K A076010 nonn,easy
%O A076010 0,2
%A A076010 _Wolfdieter Lang_, Oct 02 2002