A370509 -id:A370509 - cp's OEIS frontend

A370510 Expansion of Sum_{k>=0} k! * ( x * (1+x^3) )^k.

1, 1, 2, 6, 25, 124, 738, 5136, 40922, 367218, 3664224, 40240560, 482278326, 6263414736, 87618506160, 1313435465280, 21003904630824, 356910121855320, 6422020465846320, 121980351190294800, 2438956634267865720, 51206322309647263200, 1126314497201852150640

Offset: 0

Seiichi Manyama, Feb 20 2024

Cf. A240172, A370509.

Cf. A370508.

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^3))^k))

a(n) = sum(k=0, n\4, (n-3*k)!*binomial(n-3*k, k));

a(n) = Sum_{k=0..floor(n/4)} (n-3*k)! * binomial(n-3*k,k).

A370668 Expansion of Sum_{k>0} k! * ( x * (1+x^k) )^k.

Original entry on oeis.org

1, 3, 6, 28, 120, 740, 5040, 40416, 362898, 3629400, 39916800, 479006070, 6227020800, 87178326480, 1307674369200, 20922790210656, 355687428096000, 6402373709004720, 121645100408832000, 2432902008212929224, 51090942171709545840, 1124000727778046764800

Offset: 1

Seiichi Manyama, Feb 25 2024

nonn

Cf. A240172, A370509, A370510.

Cf. A217668.

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*(x*(1+x^k))^k))

a(n) = sumdiv(n,d, d!*binomial(d, n/d-1));

a(n) = Sum_{d|n} d! * binomial(d,n/d-1).

If p is an odd prime, a(p) = p!.

cp's OEIS Frontend

A370510 Expansion of Sum_{k>=0} k! * ( x * (1+x^3) )^k.

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula

A370668 Expansion of Sum_{k>0} k! * ( x * (1+x^k) )^k.

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula