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A049224 A convolution triangle of numbers obtained from A025751.

%I A049224 #15 Jul 04 2018 08:55:54
%S A049224 1,15,1,330,30,1,8415,885,45,1,232254,26730,1665,60,1,6735366,825858,
%T A049224 58320,2670,75,1,202060980,25992252,2003562,106560,3900,90,1,
%U A049224 6213375135,830282805,68351283,4038741,174825,5355,105,1,194685754230
%N A049224 A convolution triangle of numbers obtained from A025751.
%C A049224 a(n,1) = A025751(n); a(n,1)= 6^(n-1)*5*A034787(n-1)/n!, n >= 2.
%C A049224 G.f. for m-th column: ((1-(1-36*x)^(1/6))/6)^m.
%H A049224 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 A049224 a(n, m) = 6*(6*(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 A049224 G.f.: [(1-(1-36*x)^(1/6))/6]^m=sum(n>=m, T(n,m)*x^n), T(n,m)=(m*sum(i=m..n, binomial(-m+2*i-1,i-1)*2^(2*n-2*i)*sum(k=0..n-i, binomial(k,n-k-i)*3^(k+i-m)*(-1)^(n-k-i)*binomial(n+k-1,n-1))))/n. - _Vladimir Kruchinin_, Dec 21 2011
%o A049224 (Maxima) T(n,m):=(m*sum(binomial(-m+2*i-1,i-1)*2^(2*n-2*i)*sum(binomial(k,n-k-i)*3^(k+i-m)*(-1)^(n-k-i)*binomial(n+k-1,n-1),k,0,n-i),i,m,n))/n; /* _Vladimir Kruchinin_, Dec 21 2011 */
%Y A049224 Cf. A048966, A049223. Row sums = A025759.
%K A049224 easy,nonn,tabl
%O A049224 1,2
%A A049224 _Wolfdieter Lang_