A007182 Dimension of n-th compound of a certain space. (Formerly M1381)

1, 2, 5, 10, 23, 45, 94, 179, 358, 672, 1292, 2382, 4470, 8132, 14937, 26832, 48507, 86205, 153717, 270507, 476896, 832001, 1452283, 2513705, 4350072, 7475915, 12838338, 21919846, 37385434, 63450376, 107547996, 181525120, 305951060, 513772849, 861463730

Offset

0,2

References

Y. Chiricota, Équations différentielles combinatoires et calcul symbolique in "FPSAC5": Formal Power Series and Algebraic Combinatorics, Fifth Conference, Florence, Jun 21-25 1993, Vol. 2, p. 123.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(add(
      `if`(d<2, d, `if`(d::odd, 0, b(d/2)))*d,
       d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
    end:
a:= n-> b(2*n):
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 08 2015

Mathematica

b[n_] := b[n] = If[n==0, 1, Sum[Sum[If[d<2, d, If[OddQ[d], 0, b[d/2]]]*d, {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; a[n_] := b[2*n]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)

Crossrefs

Sequence in context: A284139 A068054 A174542 * A191386 A323988 A026677

Adjacent sequences: A007179 A007180 A007181 * A007183 A007184 A007185

Keyword

nonn

Author

Simon Plouffe

Extensions

a(0), a(17)-a(34) from Alois P. Heinz, Jul 08 2015

Status

approved