A358547 a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(n-3*k)!.

1, 1, 1, 3, 7, 13, 45, 151, 403, 1617, 6793, 23275, 105951, 522133, 2159077, 10964223, 61134955, 293587801, 1641566913, 10124731987, 55014334903, 335177088285, 2251814156701, 13587321392743, 89436553249347, 647267633012833, 4276528756374265, 30198747030078651

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..673

Formula

a(n) = (3 * (2*n-1) * a(n-1) - n * a(n-2) + 2 * (n-1) * n * (2*n-3) * a(n-3) + 2 * (2*n-3))/(9 * (n-1)) for n > 2.

a(n) ~ sqrt(Pi) * 2^(2*n/3 + 1) * n^(2*n/3 + 1/2) / (3^(2*n/3 + 3/2) * exp(2*n/3 - (2/3)^(1/3) * n^(1/3))) * (1 + 1/(2^(4/3) * 3^(5/3) * n^(1/3)) + 145/(2^(11/3) * 3^(10/3) * n^(2/3)) + 3349/(23328*n)). - Vaclav Kotesovec, Nov 25 2022

Prog

(PARI) a(n) = sum(k=0, n\3, (n-k)!/(n-3*k)!);

Crossrefs

Cf. A122852, A330044, A357532.

Sequence in context: A086208 A090968 A020641 * A062736 A257716 A103564

Adjacent sequences: A358544 A358545 A358546 * A358548 A358549 A358550

Keyword

nonn

Author

Seiichi Manyama, Nov 21 2022

Status

approved