A370581 a(n) = n! * Sum_{d|n} d/(d! * (n/d)!).

1, 3, 4, 17, 6, 307, 8, 5049, 30250, 105851, 12, 25945933, 14, 77837775, 14529715216, 147891744017, 18, 13435316294419, 20, 7606841430988821, 16895152834560022, 183030822374423, 24, 387276381308571955225, 5385836820601036800026, 485735643993600027

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Formula

If p is prime, a(p) = 1 + p.

E.g.f.: Sum_{k>0} x^k/k! * exp(x^k).

Prog

(PARI) a(n) = n!*sumdiv(n, d, d/(d!*(n/d)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/k!*exp(x^k))))

Crossrefs

Cf. A121860, A370579, A370580.

Sequence in context: A248240 A110983 A360795 * A100560 A025534 A082000

Adjacent sequences: A370578 A370579 A370580 * A370582 A370583 A370584

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 23 2024

Status

approved