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%I #11 Aug 28 2019 18:00:23
%S 1,5,1,45,5,1,585,70,5,1,9945,810,70,5,1,208845,14895,935,70,5,1,
%T 5221125,284895,16020,935,70,5,1,151412625,7055100,309645,16645,935,
%U 70,5,1,4996616625,192734100,7526475,315270,16645,935,70,5,1,184874815125
%N Triangle of numbers obtained from the partition array A134274.
%C This triangle is named S2(5)'.
%C In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.
%H W. Lang, <a href="/A134275/a134275.txt">First 10 rows and more</a>.
%F a(n,m)=sum(product(S2(5;j,1)^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. S2(5;j,1)= A007696(j) = A049029(j,1) = (4*j-3)(!^4), (quadruple- or 4-factorials).
%e [1]; [5,1]; [45,5,1]; [585,70,5,1]; [9945,810,70,5,1]; ...
%Y Cf. A134276 (row sums). A134277 (alternating row sums).
%Y Cf. A134151 (S2(4)').
%K nonn,easy,tabl
%O 1,2
%A _Wolfdieter Lang_ Nov 13 2007
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