A135593 Number of n X n symmetric (0,1)-matrices with exactly n+1 entries equal to 1 and no zero rows or columns.

2, 9, 36, 140, 540, 2142, 8624, 35856, 152280, 666380, 2982672, 13716144, 64487696, 310693320, 1528801920, 7691652992, 39474925344, 206758346256, 1103332900160, 5999356762560, 33197323465152, 186925844947424, 1069977071943936

Offset: 2

Author

Vladeta Jovovic, Feb 25 2008

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A000085, A055602, A086364.

Programs

Maple

A135593 := proc(n) n!*coeftayl( x^2*(x+2)/2*exp(x*(x+2)/2),x=0,n) ; end: seq(A135593(n),n=2..40) ; # R. J. Mathar, Mar 31 2008

Mathematica

Rest[Rest[CoefficientList[Series[x^2*(x+2)/2*E^(x*(x+2)/2), {x, 0, 20}], x]* Range[0, 20]!]] (* Vaclav Kotesovec, Oct 20 2012 *)
Flatten[{2,9,RecurrenceTable[{(n-5)*(n-2)*a[n]==(n-6)*n*a[n-1]+(n-4)*(n-1)*n*a[n-2],a[4]==36,a[5]==140},a,{n,4,20}]}] (* Vaclav Kotesovec, Oct 20 2012 *)

Formula

E.g.f.: x^2*(x+2)/2*exp(x*(x+2)/2).

Recurrence (for n>5): (n-5)*(n-2)*a(n) = (n-6)*n*a(n-1) + (n-4)*(n-1)*n*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 1/4*sqrt(2)*exp(sqrt(n)-n/2-1/4)*n^(n/2+3/2). - Vaclav Kotesovec, Oct 20 2012

Extensions

More terms from R. J. Mathar, Mar 31 2008