cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A007650 Number of set-like atomic species of degree n.

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%I A007650 M2227 #35 Dec 31 2024 06:32:21
%S A007650 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,
%T A007650 476,78,877,1,1326,1,2098,188,2745,36,5203,1,6408,477,11084,1,15687,1,
%U A007650 24709,1241,33249,1,57432,27,74529,2746,120984,1,168668,194,264075,6409,356624,1,579893,1,768857,14898,1214452,483,1669060,1
%N A007650 Number of set-like atomic species of degree n.
%D A007650 G. Labelle and P. Leroux, Identities and enumeration: weighting connected components, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896.
%D A007650 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007650 Joerg Arndt, <a href="/A007650/b007650.txt">Table of n, a(n) for n = 0..100</a>
%H A007650 S. Eberhart & N. J. A. Sloane, <a href="/A007650/a007650.pdf">Correspondence, 1977</a>
%H A007650 G. Labelle and P. Leroux, <a href="/A007649/a007649.pdf">Identities and enumeration: weighting connected components</a>, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896. (Annotated scanned copy)
%H A007650 G. Labelle and P. Leroux, <a href="https://doi.org/10.37236/1270">An extension of the exponential formula in enumerative combinatorics</a>, The Electronic Journal of Combinatorics, Volume 3, Issue 2 (1996) (The Foata Festschrift volume), Research Paper #R12.
%H A007650 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%F A007650 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
%t A007650 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 *)
%o A007650 (PARI) /* see A007649 */
%Y A007650 Cf. A005226, A007649.
%K A007650 nonn
%O A007650 0,5
%A A007650 _Simon Plouffe_
%E A007650 Added more terms, _Joerg Arndt_, Jul 30 2012