A179198 Matrix log of triangle A030528, where A030528(n,k) = C(k,n-k).

0, 1, 0, -2, 2, 0, 9, -4, 3, 0, -64, 18, -6, 4, 0, 620, -128, 27, -8, 5, 0, -7536, 1240, -192, 36, -10, 6, 0, 109032, -15072, 1860, -256, 45, -12, 7, 0, -1809984, 218064, -22608, 2480, -320, 54, -14, 8, 0, 33562944, -3619968, 327096, -30144, 3100, -384, 63, -16

Offset: 0

Author

Paul D. Hanna, Jul 09 2010

Keywords

• sign

Examples

			Triangle L begins:
0;
1,0;
-2,2,0;
9,-4,3,0;
-64,18,-6,4,0;
620,-128,27,-8,5,0;
-7536,1240,-192,36,-10,6,0;
109032,-15072,1860,-256,45,-12,7,0;
-1809984,218064,-22608,2480,-320,54,-14,8,0;
33562944,-3619968,327096,-30144,3100,-384,63,-16,9,0;
-681799680,67125888,-5429952,436128,-37680,3720,-448,72,-18,10,0;
14980204800,-1363599360,100688832,-7239936,545160,-45216,4340,-512,81,-20,11,0; ...
where column_k = (k+1)*column_0: L(n,k) = (k+1)*L(n-k,0).
		

Crossrefs

Cf. A179199 (column 0), A179200, A179201, A030528.

Programs

PARI

{L(n,k)=local(A030528=matrix(n+1,n+1,r,c,if(r>=c,binomial(c,r-c))),LOG,ID=A030528^0); LOG=sum(m=1,n+1,-(ID-A030528)^m/m);(n-k)!*LOG[n+1,k+1]}

Formula

L(n,k) = (k+1)*L(n-k,0).

E.g.f. of column 0 satisfies: G(x) = (1+x)/(1+2*x)*G(x+x^2); more formulas given in A179199.