A000432 Series-parallel numbers. (Formerly M4538 N1926)

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

3,1

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).

Links

Table of n, a(n) for n=3..40.

Formula

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

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 *)

Crossrefs

Sequence in context: A022732 A256047 A227732 * A153336 A080279 A279283

Adjacent sequences: A000429 A000430 A000431 * A000433 A000434 A000435

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved