A134151 - OEIS

%I #10 Aug 28 2019 17:36:31

%S 1,4,1,28,4,1,280,44,4,1,3640,392,44,4,1,58240,5544,456,44,4,1,

%T 1106560,80640,5992,456,44,4,1,24344320,1519840,88256,6248,456,44,4,1,

%U 608608000,31420480,1631392,90048,6248,456,44,4,1,17041024000,766525760,33293120

%N Triangle of numbers obtained from the partition array A134150.

%C This triangle is named S2(4)'.

%C In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.

%H W. Lang, <a href="/A134151/a134151.txt">First 10 rows and more</a>.

%F a(n,m)=sum(product(S2(4;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(4;j,1)= A007559(j) = A035469(j,1) = (3*j-2)!!!.

%e [1]; [4,1]; [28,4,1]; [280,44,4,1]; [3640,392,44,4,1];...

%Y Cf. A134152 (row sums). A134272 (alternating row sums).

%Y Cf. A134146 (S2(3)' triangle).

%K nonn,easy,tabl

%O 1,2

%A _Wolfdieter Lang_ Nov 13 2007