A357949 a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/k!.

1, 1, 2, 6, 25, 122, 726, 5064, 40441, 363603, 3633852, 39957180, 479364841, 6230652124, 87218228180, 1308153551160, 20929018724041, 355774626352325, 6403681619657310, 121666026312835410, 2433257739200536081, 51097345199332200726, 1124122383340449444042

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = (n-1) * a(n-1) + (n-2) * a(n-2) + (n-3) * a(n-3) + (n-6) * a(n-4) - 3 * a(n-5) - 3 * a(n-6) - 3 * a(n-7) + 4 for n > 6.

a(n) ~ n! * (1 + 1/n^3 + 3/n^4 + 7/n^5 + 31/(2*n^6) + 77/(2*n^7) + 133/n^8 + 3913/(6*n^9) + 7473/(2*n^10) + ...). - Vaclav Kotesovec, Nov 25 2022

G.f.: Sum_{k>=0} k! * x^k/(1-x^4)^(k+1). - Seiichi Manyama, Feb 26 2024

Mathematica

Table[Sum[(n-3k)!/k!, {k, 0, Floor[n/4]}], {n, 0, 30}] (* Harvey P. Dale, Apr 23 2023 *)

Prog

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

Crossrefs

Cf. A000522, A003470, A358493, A358494.

Sequence in context: A058801 A321720 A358499 * A321186 A291558 A357902

Adjacent sequences: A357946 A357947 A357948 * A357950 A357951 A357952

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 19 2022

Status

approved