A195257 O.g.f.: Sum_{n>=0} 5*(n+5)^(n-1)*x^n/(1+n*x)^n.

1, 5, 30, 185, 1180, 7845, 54850, 407225, 3241200, 27882725, 260710150, 2655929625, 29459366500, 354733101125, 4617633830250, 64677391201625, 970313455915000, 15525778234093125, 263942044676848750, 4750975877669605625, 90268637043154147500

Offset

0,2

Comments

Compare the g.f. to: W(x)^5 = Sum_{n>=0} 5*(n+5)^(n-1)*x^n/n! where W(x) = LambertW(-x)/(-x).

Compare to a g.f. of A000522: Sum_{n>=0} (n+1)^(n-1)*x^n/(1+n*x)^n, which generates the total number of arrangements of a set with n elements.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = (n-1)!*Sum_{k=1..n} 5^k/(k-1)! for n>0, with a(0)=1.

a(n) ~ 5*exp(5) * (n-1)!. - Vaclav Kotesovec, Oct 10 2020

Example

O.g.f.: A(x) = 1 + 5*x + 30*x^2 + 185*x^3 + 1180*x^4 + 7845*x^5 +...
where
A(x) = 1 + 5*x/(1+x) + 5*7*x^2/(1+2*x)^2 + 5*8^2*x^3/(1+3*x)^3 + 5*9^3*x^4/(1+4*x)^4 +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, 5*(m+5)^(m-1)*x^m/(1+m*x+x*O(x^n))^m), n)}
(PARI) {a(n)=if(n==0, 1, (n-1)!*sum(k=1, n, 5^k/(k-1)!))}

Crossrefs

Cf. A000522, A195254, A195255, A195256.

Sequence in context: A155195 A147837 A076036 * A161407 A006773 A059273

Adjacent sequences: A195254 A195255 A195256 * A195258 A195259 A195260

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2011

Status

approved