A000432 Series-parallel numbers.

8, 52, 288, 1424, 6648, 29700, 128800, 545600, 2269672, 9303140, 37672216, 150998016, 599988696, 2366216164, 9270987656, 36116062832, 139978757920, 540069059028, 2075217121688, 7944690769952, 30313624200640, 115312027433188, 437420730644304, 1655047867097280, 6247339311097296, 23530440547115428, 88447214709073696, 331832490378209152, 1242766581420901656, 4646714574562484628, 17347357264162110368, 64668460220964604944, 240747014238189337840, 895102104022837748484, 3323982608759454833032, 12329573838525875316560, 45684294664598118867184, 169098457957523787786644

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 142.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Programs

Mathematica

n = 38; s = 1/(1 - x) + O[x]^(n + 1); Do[s = s/(1 - x^k)^Coefficient[s, x^k] + O[x]^(n + 1), {k, 2, n}] ; S = s - 1; CoefficientList[4 (2 + S) (1 + S)/(1 - S)^5 + O[x]^n, x] (* Jean-François Alcover, Feb 09 2016 *)

Formula

G.f.: 4(2+S)(1+S)/(1-S)^5, where S = g.f. for A000084. - Sean A. Irvine, Nov 14 2010

Extensions

More terms from Sean A. Irvine, Nov 14 2010