A352311 Expansion of e.g.f. 1/(exp(x) - x^4/24).

1, -1, 1, -1, 2, -11, 61, -281, 1191, -5923, 41791, -354091, 2968021, -24059751, 204718515, -1996937671, 22125450621, -258434553861, 3056858429581, -37181421375349, 482010195953821, -6741275765687821, 99663246605243861, -1521712424934601901

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = binomial(n,4) * a(n-4) - Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 3.

a(n) ~ n! * 3*(-1)^n / ((1 + LambertW(3^(1/4) / 2^(5/4))) * 2^(2*n + 7) * LambertW(3^(1/4) / 2^(5/4))^(n+4)). - Vaclav Kotesovec, Mar 12 2022

a(n) = n! * Sum_{k=0..floor(n/4)} (-k-1)^(n-4*k)/(24^k*(n-4*k)!). - Seiichi Manyama, Aug 21 2024

Mathematica

m = 23; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^4/24), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^4/24)))
(PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m))*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 4);

Crossrefs

Cf. A089148, A352309, A352310.

Cf. A352304.

Sequence in context: A164034 A240548 A255549 * A275229 A074615 A126034

Adjacent sequences: A352308 A352309 A352310 * A352312 A352313 A352314

Keyword

sign

Author

Seiichi Manyama, Mar 11 2022

Status

approved