|
| |
|
|
A049224
|
|
A convolution triangle of numbers obtained from A025751.
|
|
3
| |
|
|
1, 15, 1, 330, 30, 1, 8415, 885, 45, 1, 232254, 26730, 1665, 60, 1, 6735366, 825858, 58320, 2670, 75, 1, 202060980, 25992252, 2003562, 106560, 3900, 90, 1, 6213375135, 830282805, 68351283, 4038741, 174825, 5355, 105, 1, 194685754230
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(n,1)= A025751(n); a(n,1)= 6^(n-1)*5*A034787(n-1)/n!, n >= 2. G.f. for m-th column: ((1-(1-36*x)^(1/6))/6)^m.
|
|
|
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. [From 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; [From Vladimir Kruchinin, Dec 21 2011]
|
|
|
CROSSREFS
| Cf. A048966, A049223. Row sums = A025759.
Sequence in context: A030527 A027467 A049375 * A027448 A027518 A027539
Adjacent sequences: A049221 A049222 A049223 * A049225 A049226 A049227
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
|
| |
|
|
