A179331 E.g.f. satisfies: A(x) = (1-x)/(1-3*x) * A(x*(1-x)^2).

1, 3, 21, 234, 3540, 66564, 1469412, 36584784, 998692416, 29407250880, 934026603840, 32655607021440, 1292780225168640, 57672298842359040, 2712127097197728000, 122155073614867507200, 5128063415272020787200

Offset: 1

Author

Paul D. Hanna, Jul 21 2010

Keywords

• nonn

Crossrefs

Cf. A179330.

Programs

PARI

{a(n)=local(M=matrix(n+1, n+1, r, c, if(r>=c, polcoeff(((1-x)^2+x*O(x^n))^c,r-c))), LOG, ID=M^0); LOG=sum(m=1, n+1, -(ID-M)^m/m); -n!*LOG[n+1,1]/2}

Formula

a(n) = -(-1)^n*A179330(n)/2; see A179330 for more formulas. First negative term is a(22).

Extensions

Corrected formula by Paul D. Hanna, Jul 21 2010