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%I #9 Apr 26 2023 09:23:07
%S 1,2,2,3,8,3,5,18,18,5,7,40,54,40,7,11,70,150,150,70,11,13,132,315,
%T 500,315,132,13,17,182,693,1225,1225,693,182,17,19,272,1092,3080,3430,
%U 3080,1092,272,19,23,342,1836,5460,9702,9702,5460,1836,342,23
%N Triangle T(n,m) = prime(m)*prime(n-m)*binomial(n,m) read by rows, 0<=m<=n.
%C For the purpose of this sequence define prime(0)=1.
%C Row sums are 1, 4, 14, 46, 148, 462, 1420, 4234, 12356, 34726, 95220,...
%F Symmetry: T(n,m) = T(n,n-m).
%e 1;
%e 2, 2;
%e 3, 8, 3;
%e 5, 18, 18, 5;
%e 7, 40, 54, 40, 7;
%e 11, 70, 150, 150, 70, 11;
%e 13, 132, 315, 500, 315, 132, 13;
%e 17, 182, 693, 1225, 1225, 693, 182, 17;
%e 19, 272, 1092, 3080, 3430, 3080, 1092, 272, 19;
%e 23, 342, 1836, 5460, 9702, 9702, 5460, 1836, 342, 23;
%e 29, 460, 2565, 10200, 19110, 30492, 19110, 10200, 2565, 460, 29;
%e ...
%p p:= n-> `if`(n=0, 1, ithprime(n)):
%p T:= (n, k)-> binomial(n, k)*p(k)*p(n-k):
%p seq(seq(T(n, k), k=0..n), n=0..10); # _Alois P. Heinz_, Apr 26 2023
%t Table[Table[If[n == m ==0, 1, If[m == 0 || m == n, Prime[n], (Prime[n - m]*Prime[m])*Binomial[n, m]]], {m, 0, n}], {n, 0, 10}] Flatten[%]
%Y Cf. A008578, A098350.
%K nonn,easy,tabl
%O 0,2
%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 23 2008
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