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A241869 Number of compositions of n such that the smallest part has multiplicity nine. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 09 2015, after Maple *)

CROSSREFS

Column k=9 of A238342.

Sequence in context: A219911 A056483 A056473 * A243126 A269921 A219797

Adjacent sequences:  A241866 A241867 A241868 * A241870 A241871 A241872

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Apr 30 2014

STATUS

approved

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Last modified April 6 11:51 EDT 2020. Contains 333273 sequences. (Running on oeis4.)