A351931 Expansion of e.g.f. exp(x - x^5/120).

1, 1, 1, 1, 1, 0, -5, -20, -55, -125, -125, 925, 7525, 34750, 124125, 249250, -1013375, -14708875, -97413875, -477236375, -1443329375, 3466472500, 91499089375, 804081585000, 5030009685625, 20366827624375, -23484049500625, -1391395435656875, -15503027252406875

Offset

0,7

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = n! * Sum_{k=0..floor(n/5)} (-1/5!)^k * binomial(n-4*k,k)/(n-4*k)!.

a(n) = a(n-1) - binomial(n-1,4) * a(n-5) for n > 4.

Mathematica

m = 28; Range[0, m]! * CoefficientList[Series[Exp[x - x^5/5!], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^5/5!)))
(PARI) a(n) = n!*sum(k=0, n\5, (-1/5!)^k*binomial(n-4*k, k)/(n-4*k)!);
(PARI) a(n) = if(n<5, 1, a(n-1)-binomial(n-1, 4)*a(n-5));

Crossrefs

Cf. A351929, A351930.

Cf. A275423, A351906.

Sequence in context: A008524 A055383 A090133 * A366057 A289306 A325731

Adjacent sequences: A351928 A351929 A351930 * A351932 A351933 A351934

Keyword

sign

Author

Seiichi Manyama, Feb 26 2022

Status

approved