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.

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A098625 Consider the family of multigraphs enriched by the species of derangements. Sequence gives number of those multigraphs with n loops and edges.

Original entry on oeis.org

1, 0, 2, 4, 39, 228, 2400, 23616, 307692, 4197408, 67658769, 1174316570, 22916090131, 482946085932
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

A098626 Consider the family of directed multigraphs enriched by the species of derangements. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 0, 2, 4, 57, 348, 5235, 57930, 1037540, 16842496, 363889755, 7792175070, 201054289293, 5345844537876, 162234861271288, 5156725529935952, 181284205622239755, 6713109719185427600, 269652617328843102055, 11418447984579685481310, 517839485352765454438270
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A000166, A014507, A098622, A098624, A098625, A098627.

Programs

  • PARI
    \\ R(n) is A000166 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(-x + O(x*x^n))/(1-x)}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000166. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 12 2021

A098627 Consider the family of directed multigraphs enriched by the species of derangements. Sequence gives number of those multigraphs with n labeled arcs.

Original entry on oeis.org

1, 0, 1, 2, 27, 164, 2335, 25458, 437241, 6965112, 145640817, 3057675290, 76814951587, 2003471245164, 59438049704943, 1855131250113498, 63937099992148785, 2327591284996635888, 91854272591000172321, 3828194864278619367474, 170846746588575658999147
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A000166, A014505, A098623, A098624, A098625, A098626.

Programs

  • PARI
    \\ R(n) is A000166 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(-x + O(x*x^n))/(1-x)}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014505 and 1 + R(x) is the e.g.f. of A000166. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 12 2021

A098628 Consider the family of multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 2, 12, 128, 2224, 56000, 1880832, 79985792, 4161468928, 258415579648, 18793653411840, 1576791247634432, 150745211441983488, 16253127712884269056, 1959064946185017851904, 262002352633857351942144, 38624060984664180255621120, 6240304185636529522872025088
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A000079, A014500, A098620, A098629, A098630, A098631.

Programs

  • PARI
    \\ R(n) is A000079 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={exp(2*x + O(x*x^n))}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014500 and 1 + R(x) is the e.g.f. of A000079. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A098629 Consider the family of multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n loops and edges.

Original entry on oeis.org

1, 4, 36, 528, 11392, 334624, 12677824, 596369664, 33872839680, 2274079648768, 177449470237696
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

A098630 Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 4, 60, 1624, 66240, 3711200, 269670208, 24435113216, 2682916389632, 349223324753408, 52965538033020928, 9229753832340117504, 1826647528631522463744, 406579171521484851396608, 100934277604965329345822720, 27746271707522968205726416896
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A000079, A014507, A098622, A098628, A098629, A098631.

Programs

  • PARI
    a(n) = {2^n*sum(k=0, 2*n, stirling(2*n,k,2))} \\ Andrew Howroyd, Jan 12 2021
  • PARI
    \\ R(n) is A000079 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(2*x + O(x*x^n))}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

a(n) = 2^n*Bell(2*n). - Vladeta Jovovic, Aug 22 2006
E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000079. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A098631 Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled arcs.

Original entry on oeis.org

1, 2, 28, 696, 26512, 1402656, 97017792, 8418174848, 889241719040, 111774837350912, 16420543334734848, 2778708477919836160, 535183812199464341504, 116142946557502449852416, 28156854547845767203373056, 7569375509914847295271043072, 2241898693518356603925445017600
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A000079, A014505, A020556, A098623, A098628, A098629, A098630.

Programs

  • PARI
    \\ R(n) is A000079 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(2*x + O(x*x^n))}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

a(n) = 2^n*A020556(n). - Vladeta Jovovic, Aug 11 2005
E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014505 and 1 + R(x) is the e.g.f. of A000079. - Andrew Howroyd, Jan 12 2021

Extensions

More terms from Vladeta Jovovic, Aug 11 2005
Terms a(14) and beyond from Andrew Howroyd, Jan 12 2021

A098636 Consider the family of multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled edges.

Original entry on oeis.org

1, 1, 2, 10, 78, 885, 13487, 261848, 6255453, 179297990, 6046396379, 236175330388, 10549286540957, 533103416306743, 30203144498636380, 1903491404510540902, 132543022174482851436, 10136316177816553484295, 846893706267135762556915, 76941424170126460702604994
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A014500, A098620, A098637, A098638, A098639.

Programs

  • PARI
    \\ EnrichedGnSeq defined in A098620.
EnrichedGnSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: B(sinh(x)) where B(x) is the e.g.f. of A014500. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021

A098637 Consider the family of multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n loops and edges.

Original entry on oeis.org

1, 2, 7, 45, 431, 5677, 97304, 2086120, 54337094, 1681862711, 60786960947, 2529205845825
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

A098638 Consider the family of directed multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 2, 13, 164, 3127, 82600, 2845775, 122820136, 6446913953, 402413160952, 29343933156485, 2464029760993520, 235446319553848087, 25346231173047308256, 3047931031445529965527, 406412844141860523543392, 59704680455100785101683457, 9608818815170839730520275488
Offset: 0

Views

Author

N. J. A. Sloane, Oct 26 2004

Keywords

References

  • G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Crossrefs

Cf. A014507, A098622, A098636, A098637, A098639.

Programs

  • PARI
    \\ EnrichedGdlSeq defined in A098622.
EnrichedGdlSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: exp(-1)*Sum_{n>=0}(1+sinh(x))^(n^2)/n!. - Vladeta Jovovic, Mar 04 2008
E.g.f.: B(sinh(x)) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021

Extensions

Missing a(10) inserted and terms a(13) and beyond from Andrew Howroyd, Jan 12 2021
Previous Showing 21-30 of 110 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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