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 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 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

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