A007650 Number of set-like atomic species of degree n. (Formerly M2227)

0, 1, 1, 1, 3, 1, 6, 1, 10, 4, 12, 1, 33, 1, 29, 13, 64, 1, 100, 1, 156, 30, 187, 1, 443, 10, 476, 78, 877, 1, 1326, 1, 2098, 188, 2745, 36, 5203, 1, 6408, 477, 11084, 1, 15687, 1, 24709, 1241, 33249, 1, 57432, 27, 74529, 2746, 120984, 1, 168668, 194, 264075, 6409, 356624, 1, 579893, 1, 768857, 14898, 1214452, 483, 1669060, 1

Offset

0,5

References

G. Labelle and P. Leroux, Identities and enumeration: weighting connected components, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896.

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

Links

Joerg Arndt, Table of n, a(n) for n = 0..100

S. Eberhart & N. J. A. Sloane, Correspondence, 1977

G. Labelle and P. Leroux, Identities and enumeration: weighting connected components, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896. (Annotated scanned copy)

G. Labelle and P. Leroux, An extension of the exponential formula in enumerative combinatorics, The Electronic Journal of Combinatorics, Volume 3, Issue 2 (1996) (The Foata Festschrift volume), Research Paper #R12.

N. J. A. Sloane, Transforms

Formula

Inverse Euler Transform of A007649. Define c(n): c(0)=0. c(k)=A007649(k), k>0. a=MOEBIUSi(c)-c. - Christian G. Bower, Feb 23 2006

Mathematica

NN = 66;  va = Array[0&, NN]; va[[1]] = 0; va[[2]] = 1; vm = Array[0&, NN]; vm[[1]] = 1; vm[[2]] = 1; For[n = 2, n <= NN - 1, n++, va[[n + 1]] = DivisorSum[n , vm[[#+1]]&]; vm[[n+1]] = 1/n*Sum[DivisorSum[k, #*va[[#+1]] &]*vm[[n-k+1]], {k, 1, n}]]; va (* Jean-François Alcover, Dec 01 2015, adapted from Joerg Arndt's PARI script in A007649 *)

Prog

(PARI) /* see A007649 */

Crossrefs

Cf. A005226, A007649.

Sequence in context: A360654 A145063 A202851 * A236540 A339384 A165552

Adjacent sequences: A007647 A007648 A007649 * A007651 A007652 A007653

Keyword

nonn

Author

Simon Plouffe

Extensions

Added more terms, Joerg Arndt, Jul 30 2012

Status

approved