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%I #10 Feb 09 2015 09:28:53
%S 1,0,5,5,21,35,85,175,366,730,1481,2925,5726,11110,21375,40766,77266,
%T 145495,272290,506836,938783,1730725,3176920,5808020,10578162,
%U 19197898,34725765,62616485,112574807,201827366,360885835,643679795,1145341756,2033369086
%N Number of compositions of n such that the smallest part has multiplicity four.
%H Joerg Arndt and Alois P. Heinz, <a href="/A241864/b241864.txt">Table of n, a(n) for n = 4..1000</a>
%F a(n) ~ (1/2-1/sqrt(5))^3 / 15 * n^4 * ((1+sqrt(5))/2)^n. - _Vaclav Kotesovec_, May 01 2014
%p b:= proc(n, s) option remember; `if`(n=0, 1,
%p `if`(n<s, 0, expand(add(b(n-j, s)*x, j=s..n))))
%p end:
%p a:= proc(n) local k; k:= 4;
%p add((p->add(coeff(p, x, i)*binomial(i+k, k),
%p i=0..degree(p)))(b(n-j*k, j+1)), j=1..n/k)
%p end:
%p seq(a(n), n=4..40);
%t 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=4}, 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, 4, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y Column k=4 of A238342.
%K nonn
%O 4,3
%A _Joerg Arndt_ and _Alois P. Heinz_, Apr 30 2014
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