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The programme "ALMOST OEIS A007980" installs symbolics in the Sequence Aplet to reproduce OEIS A007980 shifted upwards one place, the first element of the series being an additional zero.

https://oeis.org/A007980

This has the advantage of the series being the partial sums of

https://oeis.org/A004396

The first link above refers to

http://en.wikipedia.org/wiki/Molien_series

which perhaps rprosperi might find of some practical application?

ALMOST OEIS A007980

RUN SEQSET:
RECURSE(U,CEILING((N-1)/3*N),0,1)►U1(N):
CHECK 1:

SEQSET

SELECT Sequence:
UNCHECK 0:
0►NumFont:
0►Simult:
2►Angle:
1►InvCross:
1►NumStep:
1►Format:
1►NumCol:
1►NumStart:
6►NumRow:
RECURSE(U,0,0,0)►U1(N):
Ans►U2(N):
Ans►U3(N):
Ans►U4(N):
Ans►U5(N):
Ans►U6(N):
Ans►U7(N):
Ans►U8(N):
Ans►U9(N):
Ans►U0(N):