A219780 - OEIS

%I #5 Nov 27 2012 07:12:57

%S 1,4,26,220,2243,26484,353380,5239276,85243413,1507394980,28749072350,

%T 587631913212,12804803195383,296121904536148,7239552829750920,

%U 186477285179206924,5045665971430927721,143034320139018008196,4238027733918053839714,130967841736577170487068

%N G.f.: 1 = Sum_{n>=0} a(n) * x^n * (1 - (n+1)*x)^4.

%C Compare to: 1 = Sum_{n>=0} n! * x^n * (1 - (n+1)*x).

%C Compare to: 1 = Sum_{n>=0} A002720(n) * x^n * (1 - (n+1)*x)^2, where A002720(n) is the number of partial permutations of an n-set.

%F E.g.f.: A(x) = 1 + 4*x + 26*x^2/2! + 220*x^3/3! + 2243*x^4/4! + 26484*x^5/5! +...

%F By definition, the terms satisfy:

%F 1 = (1-x)^4 + 4*x*(1-2*x)^4 + 26*x^2*(1-3*x)^4 + 220*x^3*(1-4*x)^4 + 2243*x^4*(1-5*x)^4 + 26484*x^5*(1-6*x)^4 + 353380*x^6*(1-7*x)^4 +...

%o (PARI) {a(n)=polcoeff(1-sum(m=0, n-1, a(m)*x^m*(1-(m+1)*x+x*O(x^n))^4), n)}

%o for(n=0,25,print1(a(n),", "))

%Y Cf. A002720, A219779.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 27 2012