OFFSET
1,2
COMMENTS
First five terms [1, 7, 26, 50, 24] form row 4 of A105954 read as a triangular array.
FORMULA
a(n) = (-1)^(n-1)*24*(n - 5)! for n >= 5.
E.g.f.: A(x) = (1 + x)^4*log(1 + x).
Series reversion(A(x)) = exp(-1/4*T(-4*x)) - 1 = x - 7*x^2/2! + 11^2*x^3/3! - 15^3*x^4/4! + 19^4*x^5/5! - ... is the e.g.f. for a signed version of A274267, 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) = 2733/2275 + 1/(24*e). - Amiram Eldar, Feb 02 2023
EXAMPLE
E.g.f.= x + 7*x^2/2 + 26*x^3/3! + 50*x^4/4! + 24*x^5/5! - 24*x^6/6! + ...
MATHEMATICA
CoefficientList[Series[(1+t)^4 * Log[1+t], {t, 1, 20}], t]*Range[1, 20]! (* G. C. Greubel, Jun 19 2016 *)
PROG
(Magma) [1, 7, 26, 50] cat [(-1)^(n-1)*24*Factorial(n-5): n in [5..25]]; // Vincenzo Librandi, Jun 20 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Peter Bala, Jun 19 2016
STATUS
approved