A352304 Expansion of e.g.f. 1/(exp(x) - x^4).

1, -1, 1, -1, 25, -241, 1441, -6721, 67201, -1185409, 16652161, -180639361, 2098673281, -37526586241, 785718950017, -14516030954881, 247504017895681, -4832929862019841, 116556246644716801, -2930255897793414913, 69746855593499124481, -1673960044278244020481

Offset

0,5

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n * (n-1) * (n-2) * (n-3) * a(n-4) - Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 3.

a(n) ~ n! * (-1)^n / ((1 + LambertW(1/4)) * 2^(2*n + 10) * LambertW(1/4)^(n+4)). - Vaclav Kotesovec, Mar 12 2022

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

Mathematica

m = 21; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^4), {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)))
(PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 4);

Crossrefs

Cf. A089148, A352302, A352303.

Cf. A352300, A352311.

Sequence in context: A108178 A278849 A294290 * A362393 A107943 A125388

Adjacent sequences: A352301 A352302 A352303 * A352305 A352306 A352307

Keyword

sign

Author

Seiichi Manyama, Mar 11 2022

Status

approved