A357570 a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/(n-5*k)!.

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 14, 21, 30, 41, 60, 93, 146, 225, 336, 509, 798, 1281, 2060, 3261, 5154, 8273, 13536, 22365, 36806, 60369, 99588, 166301, 280650, 474801, 802424, 1358973, 2317806, 3987185, 6893196, 11933949, 20690738, 36022161, 63107520, 111146141, 196322454, 347412753

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

D-finite with recurrence a(n) = (4 * a(n-1) + n * a(n-5) + 1)/5 for n > 4.

Prog

(PARI) a(n) = sum(k=0, n\5, (n-4*k)!/(n-5*k)!);

Crossrefs

Cf. A072374, A122852, A357532, A357533.

Sequence in context: A307972 A346074 A211697 * A211676 A076299 A341015

Adjacent sequences: A357567 A357568 A357569 * A357571 A357572 A357573

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 19 2022

Status

approved