A219780 G.f.: 1 = Sum_{n>=0} a(n) * x^n * (1 - (n+1)*x)^4.

1, 4, 26, 220, 2243, 26484, 353380, 5239276, 85243413, 1507394980, 28749072350, 587631913212, 12804803195383, 296121904536148, 7239552829750920, 186477285179206924, 5045665971430927721, 143034320139018008196, 4238027733918053839714, 130967841736577170487068

Offset

0,2

Comments

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

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.

Links

Table of n, a(n) for n=0..19.

Formula

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

By definition, the terms satisfy:

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 +...

Prog

(PARI) {a(n)=polcoeff(1-sum(m=0, n-1, a(m)*x^m*(1-(m+1)*x+x*O(x^n))^4), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A002720, A219779.

Sequence in context: A120971 A187826 A145347 * A259902 A089816 A371539

Adjacent sequences: A219777 A219778 A219779 * A219781 A219782 A219783

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2012

Status

approved