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A241868 Number of compositions of n such that the smallest part has multiplicity eight. 2
1, 0, 9, 9, 54, 99, 309, 684, 1720, 3909, 9036, 20178, 44676, 97191, 209151, 444498, 935002, 1947729, 4021429, 8234244, 16732173, 33758283, 67656843, 134751630, 266817214, 525411981, 1029271671, 2006453683, 3893241810, 7521104292, 14468931402, 27724579185 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,3

LINKS

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..1000

FORMULA

a(n) ~ n^8 * ((1+sqrt(5))/2)^(n-17) / (5^(9/2) * 8!). - 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:= 8;

      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=8..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 = 8}, 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, 8, 40}] (* Jean-Fran├žois Alcover, Feb 09 2015, after Maple *)

CROSSREFS

Column k=8 of A238342.

Sequence in context: A014718 A339324 A145971 * A243125 A270008 A255743

Adjacent sequences:  A241865 A241866 A241867 * A241869 A241870 A241871

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Apr 30 2014

STATUS

approved

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Last modified March 8 01:41 EST 2021. Contains 341934 sequences. (Running on oeis4.)