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!)
A281361 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 9 times. 10
1, 10, 352705, 3047235458767, 609542744597785306189, 1214103036523322674154687139158, 14963835327495031822418126706099787884130, 836883118002221273912672040462907783367741190535388, 170589804359366329173961838612841486616626580885839826818966688, 107640669875812795238625627484701500354901860426640161278022882392148747562, 185260259482556646382994900799988470488841686941141661692183483756531004879305895810561 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
More than the usual number of terms are shown in the DATA field because there are the initial values needed for one of the recurrences.
LINKS
Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017.
Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix I to "Analysis of the gift exchange problem", giving Type D recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)
Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix II to "Analysis of the gift exchange problem", giving Type C recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)
David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009.
MAPLE
with(combinat):
b:= proc(n, i, t) option remember; `if`(t*i<n, 0,
`if`(n=0, `if`(t=0, 1, 0), add(b(n-i*j, i-1, t-j)*
multinomial(n, n-i*j, i$j)/j!, j=0..min(t, n/i))))
end:
a:= n-> add(b(k, 10, n), k=0..10*n):
seq(a(n), n=0..12); # Alois P. Heinz, Feb 01 2017
MATHEMATICA
t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 10*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 9}]; t[_, _] = 0; a[n_] := Sum[t[n, k], {k, 0, 10*n}]; Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Feb 18 2017 *)
PROG
(PARI) {a(n) = sum(i=n, 10*n, i!*polcoef(sum(j=1, 10, x^j/j!)^n, i))/n!} \\ Seiichi Manyama, May 22 2019
CROSSREFS
The gift scenarios sequences when a gift can be stolen at most s times, for s = 1..9, are A001515, A144416, A144508, A144509, A149187, A281358, A281359, A281360, A281361.
Sequence in context: A242854 A201548 A363197 * A177466 A069878 A235029
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 25 2017
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 March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)