A049223 A convolution triangle of numbers obtained from A025750.

1, 10, 1, 150, 20, 1, 2625, 400, 30, 1, 49875, 8250, 750, 40, 1, 997500, 174750, 17875, 1200, 50, 1, 20662500, 3780000, 419625, 32500, 1750, 60, 1, 439078125, 83128125, 9810000, 839500, 53125, 2400, 70, 1, 9513359375, 1852500000, 229359375

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn
• tabl

Comments

a(n,1) = A025750(n); a(n,1)= 5^(n-1)*4*A034301(n-1)/n!, n >= 2. G.f. for m-th column: ((1-(1-25*x)^(1/5))/5)^m.

Links

• W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Crossrefs

Cf. A048966, A049213. Row sums = A025758.

Programs

Maxima

T(n,m):=(m*sum((-1)^(n-m-3*k)*binomial(n+k-1,n-1)*sum(2^j*binomial(k,j)*sum(binomial(j,i-j)*binomial(k-j,n-m-3*(k-j)-i)*5^(3*(k-j)+i),i,j,n-m-k+j),j,0,k),k,0,n-m))/n; /* Vladimir Kruchinin, Dec 10 2011 */

Formula

a(n, m) = 5*(5*(n-1)-m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n

T(n,m) = (m*sum(k=0..n-m, (-1)^(n-m-3*k)*binomial(n+k-1,n-1)*sum(j=0..k, 2^j*binomial(k,j)*sum(i=j..n-m-k+j, binomial(j,i-j)*binomial(k-j,n-m-3*(k-j)-i)*5^(3*(k-j)+i)))))/n. - Vladimir Kruchinin, Dec 10 2011

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