A152006 Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(1) = 1 and f(m) = prime(m-1) for m >= 2.

1, 1, 2, 5, 8, 18, 34, 63, 102, 203, 336, 589, 999, 1675, 2799, 4768, 7561, 12224, 20513, 31724, 51621, 81976, 128560, 199192, 312536, 482806, 744847, 1147952, 1755931, 2649474, 4051413, 6069450, 9105323, 13747364, 20335077, 30508629, 45198631

Offset: 0

Author

Roger L. Bagula, Nov 19 2008

Keywords

• nonn

Crossrefs

Cf. A147557, A147654, A147655, A147665, A147869, A147871, A147880, A147953.

Programs

Mathematica

f[n_] = If[n < 2, n, Prime[n - 1]];
P[x_, n_] := P[x, n] = Product[1 + f[m]*x^m, {m, 0, n}];
Take[CoefficientList[P[x, 37], x],37]
(* Program edited and corrected by Petros Hadjicostas, Apr 12 2020 *)

Formula

a(n) = [x^n] Product_{k > 0} (1 + f(k)*x^k), where f(1) = 1 and f(m) = prime(m-1) for m >= 2.

Extensions

Various sections edited by Petros Hadjicostas, Apr 12 2020