OFFSET
1,2
COMMENTS
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
FORMULA
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.
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
PROG
(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 */
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved