OFFSET
1,2
COMMENTS
First four terms [1, 5, 11, 6] form row 3 of A105954 read as a triangular array.
FORMULA
a(n) = (-1)^n*6*(n - 4)! for n >= 4.
E.g.f.: A(x) = (1 + x)^3*log(1 + x).
Series reversion(A(x)) = exp(-1/3*T(-3*x)) - 1 = x - 5*x^2/2! + 8^2*x^3/3! - 11^3*x^4/4! + 14^4*x^5/5! - ... is the e.g.f. for a signed version of A274265, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is Euler's tree function - see A000169.
Sum_{n>=1} 1/a(n) = 71/55 + 1/(6*e). - Amiram Eldar, Feb 02 2023
EXAMPLE
E.g.f.= x + 5*x^2/2 + 11*x^3/3! + 6*x^4/4! - 6*x^5/5! + ....
MATHEMATICA
CoefficientList[Series[(1+t)^3 * Log[1+t], {t, 1, 20}], t]*Range[1, 20]! (* G. C. Greubel, Jun 19 2016 *)
PROG
(Magma) [1, 5, 11] cat [(-1)^n*6*Factorial(n-4): n in [4..25]]; // Vincenzo Librandi, Jun 20 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Peter Bala, Jun 19 2016
STATUS
approved