The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A357949 a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/k!. 2
1, 1, 2, 6, 25, 122, 726, 5064, 40441, 363603, 3633852, 39957180, 479364841, 6230652124, 87218228180, 1308153551160, 20929018724041, 355774626352325, 6403681619657310, 121666026312835410, 2433257739200536081, 51097345199332200726, 1124122383340449444042 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Sequence in context: A058801 A321720 A358499 * A321186 A291558 A357902
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 19 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)