A049224 A convolution triangle of numbers obtained from A025751.

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

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

Table of n, a(n) for n=1..37.

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

Cf. A048966, A049223. Row sums = A025759.

Sequence in context: A030527 A027467 A049375 * A223517 A027448 A027518

Adjacent sequences: A049221 A049222 A049223 * A049225 A049226 A049227

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved