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A241865 Number of compositions of n such that the smallest part has multiplicity five. 2
1, 0, 6, 6, 27, 49, 125, 258, 579, 1202, 2512, 5157, 10463, 20949, 41627, 81912, 159834, 309641, 595836, 1139211, 2165502, 4094219, 7701857, 14420351, 26880988, 49902183, 92279657, 170020844, 312173822, 571307477, 1042310911, 1896039086, 3439404321, 6222483152 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,3

LINKS

Joerg Arndt, Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 5..1500 (first 1000 terms from Joerg Arndt and Alois P. Heinz)

FORMULA

a(n) ~ n^5 * ((1+sqrt(5))/2)^(n-11) / (5^3 * 5!). - 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:= 5;

      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=5..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 = 5}, 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, 5, 40}] (* Jean-Fran├žois Alcover, Feb 09 2015, after Maple *)

CROSSREFS

Column k=5 of A238342.

Sequence in context: A255466 A286482 A123874 * A243122 A274940 A253066

Adjacent sequences:  A241862 A241863 A241864 * A241866 A241867 A241868

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Apr 30 2014

STATUS

approved

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)