A093733 Number of connected relations.

1, 665, 106819, 10365005, 805351531, 56294206205, 3735873535339, 241600284318365, 15423235216318411, 978180744322139645, 61834480769377286059, 3902270609960140639325, 246057483524862034206091, 15508484277325946034039485, 977254123876968508188975979

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..100

Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

G. Kreweras, Inversion des polynômes de Bell bidimensionnels et application au dénombrement des relations binaires connexes, C. R. Acad. Sci. Paris Ser. A-B 268 1969 A577-A579.

Index entries for linear recurrences with constant coefficients, signature (-195, 15886, -726290, 20952193, -403792115, 5336718048, -48588590600, 299693200656, -1195947048240, 2785165036416, -2872859996160).

Formula

a(n) = 63^n - 6*32^n - 15*18^n + 30*17^n - 10*14^n + 120*11^n - 120*10^n + 30*9^n - 270*8^n + 360*7^n - 120*6^n.

G.f.: x*(96368590080*x^9 + 27682953984*x^8 - 13185435000*x^7 + 774468980*x^6 + 143028190*x^5 - 19071533*x^4 + 626800*x^3 + 6970*x^2 - 470*x - 1) / ((6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(14*x -1)*(17*x -1)*(18*x -1)*(32*x -1)*(63*x -1)). - Colin Barker, Jul 07 2013

Mathematica

Table[63^n-6*32^n-15*18^n+30*17^n-10*14^n+120*11^n-120*10^n+30*9^n-270*8^n+360*7^n-120*6^n, {n, 1, 25}] (* G. C. Greubel, Oct 06 2017 *)
CoefficientList[Series[x (96368590080x^9+27682953984x^8-13185435000x^7+774468980x^6+ 143028190x^5-19071533x^4+626800x^3+6970x^2-470x-1)/((6x-1)(7x-1)(8x-1)(9x-1)(10x-1)(11x-1)(14x-1)(17x-1)(18x-1)(32x-1)(63x-1)), {x, 0, 20}], x] (* or *) LinearRecurrence[{195, -15886, 726290, -20952193, 403792115, -5336718048, 48588590600, -299693200656, 1195947048240, -2785165036416, 2872859996160}, {0, 1, 665, 106819, 10365005, 805351531, 56294206205, 3735873535339, 241600284318365, 15423235216318411, 978180744322139645}, 20] (* Harvey P. Dale, Sep 23 2023 *)

Prog

(PARI) for(n=1, 25, print1(63^n-6*32^n-15*18^n+30*17^n-10*14^n+120*11^n-120*10^n+30*9^n-270*8^n+360*7^n-120*6^n, ", ")) \\ G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A001047, A002501, A002502, A005333, A093732.

Sequence in context: A211839 A171395 A069426 * A133562 A202445 A062045

Adjacent sequences: A093730 A093731 A093732 * A093734 A093735 A093736

Keyword

nonn,easy

Author

Goran Kilibarda and Vladeta Jovovic, Apr 14 2004

Status

approved