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

0,4

Links

Table of n, a(n) for n=0..52.

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.

Example

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).

Prog

(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]}

Crossrefs

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

Sequence in context: A009615 A184011 A079194 * A372390 A117739 A243203

Adjacent sequences: A179195 A179196 A179197 * A179199 A179200 A179201

Keyword

sign

Author

Paul D. Hanna, Jul 09 2010

Status

approved