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A158876 E.g.f.: exp( Sum_{n>=1} (n-1)! * x^n ). 5
1, 1, 3, 19, 217, 4041, 113611, 4532683, 244208049, 17085010897, 1504881245971, 162835665686211, 21219897528855433, 3276502399914104089, 591351260856215820507, 123322423833602768272891, 29423834155886520870184801, 7963056392690313008566254753 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..253

FORMULA

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

E.g.f. A(x) satisfies:

(1) A'(x)/A(x) = Sum_{k>=0} (n+1)! * x^n.

(2) A(x) = exp(x + x^2 * A'(x)/A(x)).

Let F(x) = Sum_{n>=0} n! * x^n, then

(3) [x^n] A(x)^n * (2 - F(x)) = 0 for n > 0,

(4) [x^n] A(x) * (n + 1 - F(x)) = 0 for n > 0. - Paul D. Hanna, May 26 2018

a(n) ~ n! * (n-1)!. - Vaclav Kotesovec, Aug 01 2017

EXAMPLE

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 217*x^4/4! +...

log(A(x)) = x + x^2 + 2!*x^3 + 3!*x^4 +...+ (n-1)!*x^n +....

PROG

(PARI) {a(n)=if(n==0, 1, (n-1)!*sum(k=1, n, k!*a(n-k)/(n-k)!))}

for(n=0, 20, print1(a(n), ", "))

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

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A000142, A122949.

Sequence in context: A230317 A135749 A005647 * A001833 A001035 A267634

Adjacent sequences:  A158873 A158874 A158875 * A158877 A158878 A158879

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 13 2009

STATUS

approved

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Last modified July 17 07:23 EDT 2018. Contains 312694 sequences. (Running on oeis4.)