%I #15 Jul 04 2018 08:55:46

%S 1,10,1,150,20,1,2625,400,30,1,49875,8250,750,40,1,997500,174750,

%T 17875,1200,50,1,20662500,3780000,419625,32500,1750,60,1,439078125,

%U 83128125,9810000,839500,53125,2400,70,1,9513359375,1852500000,229359375

%N A convolution triangle of numbers obtained from A025750.

%C a(n,1) = A025750(n); a(n,1)= 5^(n-1)*4*A034301(n-1)/n!, n >= 2. G.f. for m-th column: ((1-(1-25*x)^(1/5))/5)^m.

%H W. Lang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

%F a(n, m) = 5*(5*(n-1)-m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1.

%F T(n,m) = (m*sum(k=0..n-m, (-1)^(n-m-3*k)*binomial(n+k-1,n-1)*sum(j=0..k, 2^j*binomial(k,j)*sum(i=j..n-m-k+j, binomial(j,i-j)*binomial(k-j,n-m-3*(k-j)-i)*5^(3*(k-j)+i)))))/n. - _Vladimir Kruchinin_, Dec 10 2011

%o (Maxima)

%o T(n,m):=(m*sum((-1)^(n-m-3*k)*binomial(n+k-1,n-1)*sum(2^j*binomial(k,j)*sum(binomial(j,i-j)*binomial(k-j,n-m-3*(k-j)-i)*5^(3*(k-j)+i),i,j,n-m-k+j),j,0,k),k,0,n-m))/n; /* _Vladimir Kruchinin_, Dec 10 2011 */

%Y Cf. A048966, A049213. Row sums = A025758.

%K easy,nonn,tabl

%O 1,2

%A _Wolfdieter Lang_