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!)
A361571 Expansion of e.g.f. exp( (x * (1+x))^3 ). 1
1, 0, 0, 6, 72, 360, 1080, 15120, 302400, 3689280, 32659200, 359251200, 6965481600, 133880947200, 2070484416000, 30305353478400, 559684629504000, 12582442768896000, 271843009108070400, 5401042458152140800, 111578968350001152000, 2657164887872022528000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(3*k,n-3*k)/k!.
a(0) = 1; a(n) = (n-1)! * Sum_{k=3..n} k * binomial(3,k-3) * a(n-k)/(n-k)!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(1+x))^3)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=3, i, j*binomial(3, j-3)*v[i-j+1]/(i-j)!)); v;
CROSSREFS
Cf. A361279.
Sequence in context: A250071 A192990 A276244 * A282817 A274955 A177468
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 16 2023
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 June 21 04:30 EDT 2024. Contains 373540 sequences. (Running on oeis4.)