A147879 Expansion of Product_{k>=1} (1 + x^k*A005185(k)).

1, 1, 1, 3, 5, 8, 12, 21, 29, 49, 73, 105, 162, 236, 338, 502, 706, 984, 1441, 1998, 2800, 3934, 5472, 7407, 10210, 14053, 19066, 25986, 35134, 47010, 63739, 85008, 112610, 150861, 200133, 264838, 349587, 459970, 602763, 792220, 1034136, 1345530

Offset: 0

Author

Roger L. Bagula, Nov 16 2008

Keywords

• nonn

Crossrefs

Cf. A004001, A005185, A147559, A147654, A147655, A147665, A147869, A147871.

Programs

Mathematica

f[n_Integer?Positive] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]]; f[0] = 0; f[1] = f[2] = 1; (* A005185 *)
nmax = 41; CoefficientList[Series[Product[(1 + f[k] * x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Georg Fischer, Dec 10 2020 *)

PARI

\\ here B(n) is A005185 as vector.
B(n)={my(A=vector(n, k, 1)); for(k=3, n, A[k]= A[k-A[k-1]]+ A[k-A[k-2]]); A}
seq(n)=my(v=B(n)); {Vec(prod(k=1, #v, 1 + x^k*v[k] + O(x*x^n)))} \\ Andrew Howroyd, Dec 10 2020

Extensions

Definition corrected by Georg Fischer, Dec 10 2020