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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.)