login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A249584 E.g.f.: Sum_{n>=0} (1 - exp(-n^n*x))^n. 0
1, 1, 31, 117715, 103060086811, 35762522984596014091, 7426384178532990386136937008571, 1294894823429942167077615079432957932604708795, 253092741940931724342360814670783323840910439695820558059377771, 71352024076415778396125047299738711969981288880155877082517115026490261985701403851 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) == 1 (mod 6) for n>=0.

LINKS

Table of n, a(n) for n=0..9.

FORMULA

O.g.f.: Sum_{n>=0} n^(n^2) * n! * x^n / Product_{k=1..n} (1 + n^n*k*x).

a(n) = Sum_{k=0..n} (-1)^(n-k) * (k^k)^n * k! * Stirling2(n,k).

a(n) ~ n! * n^(n^2). - Vaclav Kotesovec, Aug 24 2017

EXAMPLE

E.g.f.: A(x) = 1 + x + 31*x^2/2! + 117715*x^3/3! + 103060086811*x^4/4! +...

where

A(x) = 1 + (1-exp(-x)) + (1-exp(-2^2*x))^2 + (1-exp(-3^3*x))^3 + (1-exp(-4^4*x))^4 + (1-exp(-5^5*x))^5 + (1-exp(-6^6*x))^6 +...

Ordinary generating function.

O.g.f.: F(x) = 1 + x + 31*x^2 + 117715*x^3 + 103060086811*x^4 +...

where

F(x) = 1 + x/(1+x) + 2^4*2!*x^2/((1+2^2*1*x)*(1+2^2*2*x)) + 3^9*3!*x^3/((1+3^3*1*x)*(1+3^3*2*x)*(1+3^3*3*x)) + 4^16*4!*x^4/((1+4^4*1*x)*(1+4^4*2*x)*(1+4^4*3*x)*(1+4^4*4*x)) + 5^25*5!*x^5/((1+5^5*1*x)*(1+5^5*2*x)*(1+5^5*3*x)*(1+5^5*4*x)*(1+5^5*5*x)) +...

MATHEMATICA

Flatten[{1, Table[Sum[(-1)^(n-k)*(k^k)^n*k!*StirlingS2[n, k], {k, 1, n}], {n, 1, 10}]}] (* Vaclav Kotesovec, Aug 24 2017 *)

PROG

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

for(n=0, 15, print1(a(n), ", "))

(PARI) {a(n)=polcoeff(sum(m=0, n, m^(m^2)*m!*x^m/prod(k=1, m, 1+m^m*k*x +x*O(x^n))), n)}

for(n=0, 15, print1(a(n), ", "))

(PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}

{a(n) = sum(k=0, n, (-1)^(n-k)*k^(k*n)*k!*Stirling2(n, k))}

for(n=0, 10, print1(a(n), ", "))

CROSSREFS

Cf. A220181, A187755, A203798.

Sequence in context: A188956 A218142 A117579 * A107122 A059113 A057839

Adjacent sequences:  A249581 A249582 A249583 * A249585 A249586 A249587

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 01 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 18 10:21 EDT 2021. Contains 343087 sequences. (Running on oeis4.)