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

2,1

Links

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

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

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 *)

Crossrefs

Cf. A000085, A055602, A086364.

Sequence in context: A288834 A134759 A007946 * A027995 A077836 A003125

Adjacent sequences: A135590 A135591 A135592 * A135594 A135595 A135596

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 25 2008

Extensions

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

Status

approved