|
| |
|
|
A049213
|
|
A convolution triangle of numbers obtained from A025749.
|
|
4
| |
|
|
1, 6, 1, 56, 12, 1, 616, 148, 18, 1, 7392, 1904, 276, 24, 1, 93632, 25312, 4080, 440, 30, 1, 1230592, 344960, 59808, 7360, 640, 36, 1, 16612992, 4792128, 876960, 118224, 11960, 876, 42, 1, 228890112, 67586816, 12900416, 1860992, 209200, 18096, 1148
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(n,1) = A025749(n); a(n,1)= 4^(n-1)*3*A034176(n-1)/n!, n >= 2. G.f. for m-th column: ((1-(1-16*x)^(1/4))/4)^m.
|
|
|
LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
|
|
|
FORMULA
| a(n, m) = 4*(4*(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.
a(n,m) = m/n * 4^(n-m) * sum(k=1..n-m, binomial(n+k-1,n-1) * sum(j=0..k, binomial(j,n-m-3*k+2*j) * 4^(j-k) * binomial(k,j) * 3^(-n+m+3*k-j) * 2^(n-m-3*k+j) * (-1)^(n-m-3*k+2*j))), n>m; a(n,n)=1. [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Feb 08 2011]
|
|
|
CROSSREFS
| Cf. A048966. Row sums = A025757.
Sequence in context: A090435 A136237 A083837 * A165886 A174502 A056218
Adjacent sequences: A049210 A049211 A049212 * A049214 A049215 A049216
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
|
| |
|
|
