A006296 Number of genus 1 rooted maps with 3 faces with n vertices. (Formerly M5341)

70, 1720, 24164, 256116, 2278660, 17970784, 129726760, 875029804, 5593305476, 34225196720, 201976335288, 1156128848680, 6447533938280, 35155923872640, 187959014565840, 987658610225052, 5110652802256260, 26084524995672080, 131501187454625560, 655590388845975000, 3235463376771463288, 15820770680078552000, 76708503479715247920, 369046200766330733880, 1762793459781859039080, 8364468224596427692896, 39445646133672676352560, 184956513528952419546448, 862615498961026097997392, 4003067488703222112053760, 18489846573354278755829152, 85028133934182275077421180, 389398354121840111751946628, 1776360539933013004774353872, 8073622060225813990245976280, 36567311475673299914222851832

Offset

4,1

References

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

T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..1000

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.

Notes

Formula

G.f.: x(1-sqrt(1-4*x))(45+152*x+(25+8*x)sqrt(1-4*x))/(2(1-4*x)^(11/2)). - Sean A. Irvine, Nov 14 2010

Mathematica

Rest[CoefficientList[Series[(1 - Sqrt[1 - 4 x]) (45 + 152 x + (25 + 8 x) Sqrt[1 - 4 x]) / (2 (1 - 4 x)^(11 / 2)), {x, 0, 40}], x]] (* Vincenzo Librandi, Jun 06 2017 *)

Prog

(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A006296_ser(N) = {
  my(y = A000108_ser(N+1));
  -2*y*(y-1)^4*(10*y^3 + 97*y^2 - 64*y - 8)/(y-2)^11;
};
Vec(A006296_ser(36)) \\ Gheorghe Coserea, Jun 04 2017

Crossrefs

Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, this sequence, A288071 f=4, A288072 f=5, A287046 f=6, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.

Column 3 of A269921, column g=1 of A270407.

Sequence in context: A278548 A107421 A076430 * A047835 A133312 A333967

Adjacent sequences: A006293 A006294 A006295 * A006297 A006298 A006299

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved