|
| |
|
|
A072576
|
|
Limit of number of compositions (ordered partitions) of m into distinct parts where largest part is exactly m-n, for m sufficiently large given n.
|
|
4
|
|
|
|
1, 2, 2, 8, 8, 14, 38, 44, 68, 98, 242, 272, 440, 590, 878, 1772, 2180, 3194, 4466, 6320, 8432, 16190, 19262, 28580, 38276, 54314, 70730, 99152, 163328, 204230, 286670, 386132, 527132, 695978, 941738, 1220984, 1950128, 2390294, 3321398, 4342148, 5929532, 7616642, 10284410
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for sequences related to compositions
|
|
|
FORMULA
|
a(n) = Sum_k (k+1)! * A060016(n,k) = Sum_k (k+1) * A072574(n,k).
a(n) = Sum_k (k+1)! * A008289(n,k). - Alois P. Heinz, Dec 12 2012
|
|
|
EXAMPLE
|
a(3) = 8 because for any m>6 the number of compositions of e.g. m=7 into distinct parts where the largest part is exactly m-3=7-3=4 is eight, since 7 can be written as 4+3 =4+2+1 =4+1+2 =3+4 =2+4+1 =2+1+4 =1+4+2 =1+2+4.
|
|
|
MAPLE
|
b:= proc(n, i) b(n, i):= `if`(n=0, [1], `if`(i<1, [], zip((x, y)
-> x+y, b(n, i-1), `if`(i>n, [], [0, b(n-i, i-1)[]]), 0))) end:
a:= proc(n) local l; l:= b(n, n): add ( i! * l[i], i=1..nops(l)) end:
seq (a(n), n=0..50); # Alois P. Heinz, Dec 12 2012
|
|
|
PROG
|
(PARI)
N=66; q='q+O('q^N);
gf=sum(n=0, N, (n+1)!*q^(n*(n+1)/2) / prod(k=1, n, 1-q^k ) );
Vec(gf)
/* Joerg Arndt, Oct 20 2012 */
|
|
|
CROSSREFS
|
Cf. A072575.
Cf. A032020. - Alois P. Heinz, Dec 12 2012
Sequence in context: A187791 A151924 A058524 * A060818 A082887 A137583
Adjacent sequences: A072573 A072574 A072575 * A072577 A072578 A072579
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Henry Bottomley, Jun 21 2002
|
|
|
STATUS
|
approved
|
| |
|
|
