OFFSET
5,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 5..1000
FORMULA
a(n) = 30*a(n-1) - 380*a(n-2) + 2690*a(n-3) - 11944*a(n-4) + 35618*a(n-5) - 74912*a(n-6) + 115104*a(n-7) - 132120*a(n-8) + 114500*a(n-9) - 74888*a(n - 10) + 36504*a(n - 11) - 12888*a(n - 12) + 3120*a(n - 13) - 464*a(n - 14) + 32*a(n - 15). - Vaclav Kotesovec, Oct 14 2017
a(n) ~ c * d^n, where d = 7.72502395887257562679242875427350515911685429396536... is the real root of the equation -2 + 10*d - 20*d^2 + 20*d^3 - 10*d^4 + d^5 = 0 and c = 0.67250239588725756267924287542735051591168542939653... is the real root of the equation -1 - 50*c - 1000*c^2 - 10000*c^3 - 50000*c^4 + 100000*c^5 = 0. - Vaclav Kotesovec, Oct 15 2017
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1,
add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
end:
a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(5):
seq(a(n), n=5..30);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == 0, 1,
Sum[b[n - j, k] Binomial[j + k - 1, k - 1], {j, 1, n}]];
a[n_] := With[{k = 5}, Sum[b[n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]];
a /@ Range[5, 30] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 12 2017
STATUS
approved