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A179198 Matrix log of triangle A030528, where A030528(n,k) = C(k,n-k). 1

%I

%S 0,1,0,-2,2,0,9,-4,3,0,-64,18,-6,4,0,620,-128,27,-8,5,0,-7536,1240,

%T -192,36,-10,6,0,109032,-15072,1860,-256,45,-12,7,0,-1809984,218064,

%U -22608,2480,-320,54,-14,8,0,33562944,-3619968,327096,-30144,3100,-384,63,-16

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

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

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

%e Triangle L begins:

%e 0;

%e 1,0;

%e -2,2,0;

%e 9,-4,3,0;

%e -64,18,-6,4,0;

%e 620,-128,27,-8,5,0;

%e -7536,1240,-192,36,-10,6,0;

%e 109032,-15072,1860,-256,45,-12,7,0;

%e -1809984,218064,-22608,2480,-320,54,-14,8,0;

%e 33562944,-3619968,327096,-30144,3100,-384,63,-16,9,0;

%e -681799680,67125888,-5429952,436128,-37680,3720,-448,72,-18,10,0;

%e 14980204800,-1363599360,100688832,-7239936,545160,-45216,4340,-512,81,-20,11,0; ...

%e where column_k = (k+1)*column_0: L(n,k) = (k+1)*L(n-k,0).

%o (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]}

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

%K sign

%O 0,4

%A _Paul D. Hanna_, Jul 09 2010

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)