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A049223 A convolution triangle of numbers obtained from A025750. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..39.

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

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<m; a(n, 0) := 0; a(1, 1)=1.

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

PROG

(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 */

CROSSREFS

Cf. A048966, A049213. Row sums = A025758.

Sequence in context: A048882 A192357 A156286 * A308282 A223512 A131367

Adjacent sequences:  A049220 A049221 A049222 * A049224 A049225 A049226

KEYWORD

easy,nonn,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)