A361569 Expansion of e.g.f. exp(x^4/24 * (1+x)^4).

1, 0, 0, 0, 1, 20, 180, 840, 1715, 2520, 88200, 1940400, 29111775, 303603300, 2188286100, 12549537000, 143029511625, 3397035642000, 71419225878000, 1170096883956000, 15075357741068625, 163540869094102500, 2025016641129982500, 40912918773391665000

Offset

0,6

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} binomial(4*k,n-4*k)/(24^k * k!).

a(0) = 1; a(n) = ((n-1)!/24) * Sum_{k=4..n} k * binomial(4,k-4) * a(n-k)/(n-k)!.

a(n) = (n-1)*(n-2)*(n-3)/24 * (4*a(n-4) + 20*(n-4)*a(n-5) + 36*(n-4)*(n-5)*a(n-6) + 28*(n-4)*(n-5)*(n-6)*a(n-7) + 8*(n-4)*(n-5)*(n-6)*(n-7)*a(n-8)). -Seiichi Manyama, Jun 16 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^4/24*(1+x)^4)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/24*sum(j=4, i, j*binomial(4, j-4)*v[i-j+1]/(i-j)!)); v;

Crossrefs

Cf. A047974, A361567, A361568.

Cf. A361280.

Sequence in context: A159538 A091983 A037250 * A000144 A361609 A219581

Adjacent sequences: A361566 A361567 A361568 * A361570 A361571 A361572

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2023

Status

approved