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.

A059947 Number of 6-block bicoverings of an n-set.

This page as a plain text file.
%I A059947 #24 Jan 29 2020 19:35:39
%S A059947 0,0,0,3,256,7255,149660,2681063,44659776,714287535,11154475420,
%T A059947 171673613023,2618246526896,39701554817015,599773397512380,
%U A059947 9038881598035383,136004367641775616,2044264589908169695,30705868769902628540,461006369270166660143,6919274132365824549936
%N A059947 Number of 6-block bicoverings of an n-set.
%D A059947 I. P. Goulden and D. M.Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
%H A059947 Georg Fischer, <a href="/A059947/b059947.txt">Table of n, a(n) for n = 1..500</a>
%H A059947 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (48,-932,9550,-56319,194762,-382908,387000,-151200).
%F A059947 a(n) = (1/6!)*(15^n - 6*10^n - 15*7^n + 30*6^n + 60*4^n - 50*3^n - 180*2^n + 240).
%F A059947 E.g.f.: exp(-x-1/2*x^2*(exp(y)-1)) * Sum_{i>=0} x^i/i!*exp(binomial(i, 2)*y), for m-block bicoverings of an n-set.
%F A059947 G.f.: x^4*(16800*x^4-11362*x^3+2237*x^2-112*x-3) / ((1-x)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(7*x-1)*(10*x-1)*(15*x-1)). [_Colin Barker_, Jan 11 2013; corrected by _Georg Fischer_, May 18 2019]
%t A059947 CoefficientList[Series[x^4*(16800*x^4-11362*x^3+2237*x^2-112*x-3) / ((1-x)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)*(7*x-1)*(10*x-1)*(15*x-1)), {x, 0, 21}], x] (* _Georg Fischer_, May 18 2019 *)
%o A059947 (PARI) a(n)=(1/6!)*(15^n-6*10^n-15*7^n+30*6^n+60*4^n-50*3^n-180*2^n+240) \\ _Georg Fischer_, May 18 2019
%Y A059947 Column k=6 of A059443.
%Y A059947 Cf. A002718.
%K A059947 easy,nonn
%O A059947 1,4
%A A059947 _Vladeta Jovovic_, Feb 14 2001
%E A059947 More terms from _Colin Barker_, Jan 11 2013