login
A351754
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x/(1 - x)) / (1 - x)^2.
1
1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 129, 277, 651, 1703, 4859, 14581, 44711, 138053, 427709, 1334461, 4226501, 13724063, 46110643, 161210421, 586729441, 2213187623, 8591628435, 34081480017, 137398121611, 561199251633, 2320442726999, 9722362801575
OFFSET
0,7
FORMULA
a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-4,k+1) * a(k).
MATHEMATICA
nmax = 32; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 5, 1, Sum[Binomial[n - 4, k + 1] a[k], {k, 0, n - 5}]]; Table[a[n], {n, 0, 32}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 18 2022
STATUS
approved