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A241868
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Number of compositions of n such that the smallest part has multiplicity eight.
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2
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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
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OFFSET
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8,3
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LINKS
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FORMULA
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a(n) ~ n^8 * ((1+sqrt(5))/2)^(n-17) / (5^(9/2) * 8!). - Vaclav Kotesovec, May 02 2014
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MAPLE
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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);
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MATHEMATICA
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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-François Alcover, Feb 09 2015, after Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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