A223511 Triangle T(n,k) represents the coefficients of (x^9*d/dx)^n, where n=1,2,3,...;generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

1, 9, 1, 153, 27, 1, 3825, 855, 54, 1, 126225, 32895, 2745, 90, 1, 5175225, 1507815, 150930, 6705, 135, 1, 253586025, 80565975, 9205245, 499590, 13860, 189, 1, 14454403425, 4926412575, 623675430, 39180645, 1345050, 25578, 252, 1

Offset: 1

Author

Udita Katugampola, Mar 23 2013

Keywords

• nonn
• easy
• tabl

Comments

Also the Bell transform of A045755(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016

Examples

			1;
9,1;
153,27,1;
3825,855,54,1;
126225,32895,2745,90,1;
5175225,1507815,150930,6705,135,1;
253586025,80565975,9205245,499590,13860,189,1;
14454403425,4926412575,623675430,39180645,1345050,25578,252,1;
		

Crossrefs

Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223512-A223522, A223168-A223172, A223523-A223532.

Programs

Maple

b[0]:=g(x):
for j from 1 to 10 do
b[j]:=simplify(x^9*diff(b[j-1],x$1);
end do;
# The function BellMatrix is defined in A264428.
# Adds (1,0,0,0, ..) as column 0.
BellMatrix(n -> mul(8*k+1, k=0..n), 10); # Peter Luschny, Jan 29 2016

Mathematica

rows = 8;
t = Table[Product[8k+1, {k, 0, n}], {n, 0, rows}];
T[n_, k_] := BellY[n, k, t];
Table[T[n, k], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 22 2018, after Peter Luschny *)