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A241867 Number of compositions of n such that the smallest part has multiplicity seven.

%I A241867 #10 Feb 09 2015 09:29:10
%S A241867 1,0,8,8,44,80,236,513,1238,2744,6160,13384,28846,61228,128513,266668,
%T A241867 548185,1116580,2255452,4521198,8998844,17792361,34962224,68305274,
%U A241867 132724871,256587512,493665604,945497642,1803122075,3424720416,6479635254,12214748337
%N A241867 Number of compositions of n such that the smallest part has multiplicity seven.
%H A241867 Joerg Arndt and Alois P. Heinz, <a href="/A241867/b241867.txt">Table of n, a(n) for n = 7..1000</a>
%F A241867 a(n) ~ n^7 * ((1+sqrt(5))/2)^(n-15) / (5^4 * 7!). - _Vaclav Kotesovec_, May 02 2014
%p A241867 b:= proc(n, s) option remember; `if`(n=0, 1,
%p A241867       `if`(n<s, 0, expand(add(b(n-j, s)*x, j=s..n))))
%p A241867     end:
%p A241867 a:= proc(n) local k; k:= 7;
%p A241867       add((p->add(coeff(p, x, i)*binomial(i+k, k),
%p A241867        i=0..degree(p)))(b(n-j*k, j+1)), j=1..n/k)
%p A241867     end:
%p A241867 seq(a(n), n=7..40);
%t A241867 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 = 7}, 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, 7, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A241867 Column k=7 of A238342.
%K A241867 nonn
%O A241867 7,3
%A A241867 _Joerg Arndt_ and _Alois P. Heinz_, Apr 30 2014