A241869 Number of compositions of n such that the smallest part has multiplicity nine.

1, 0, 10, 10, 65, 120, 395, 890, 2320, 5401, 12847, 29380, 66735, 148630, 327270, 711247, 1529020, 3252775, 6855276, 14320645, 29672905, 61018010, 124587120, 252694835, 509337682, 1020610708, 2033777830, 4031514561, 7951981550, 15611183177, 30510678865

Offset

9,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..1000

Formula

a(n) ~ n^9 * ((1+sqrt(5))/2)^(n-19) / (5^5 * 9!). - Vaclav Kotesovec, May 02 2014

Maple

b:= proc(n, s) option remember; `if`(n=0, 1,
      `if`(n<s, 0, expand(add(b(n-j, s)*x, j=s..n))))
    end:
a:= proc(n) local k; k:= 9;
      add((p->add(coeff(p, x, i)*binomial(i+k, k),
       i=0..degree(p)))(b(n-j*k, j+1)), j=1..n/k)
    end:
seq(a(n), n=9..40);

Mathematica

b[n_, s_] := b[n, s] = If[n == 0, 1, If[n<s, 0, Expand[Sum[b[n-j, s]*x, {j, s, n}] ]]]; a[n_] := With[{k=9}, Sum[Function[{p}, Sum[Coefficient[p, x, i]*Binomial[i+k, k], {i, 0, Exponent[p, x]}]][b[n-j*k, j+1]], {j, 1, n/k}]]; Table[ a[n], {n, 9, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=9 of A238342.

Sequence in context: A219911 A056483 A056473 * A243126 A377189 A269921

Adjacent sequences: A241866 A241867 A241868 * A241870 A241871 A241872

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved