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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.

%I A223511 #14 Jun 22 2018 09:22:47
%S A223511 1,9,1,153,27,1,3825,855,54,1,126225,32895,2745,90,1,5175225,1507815,
%T A223511 150930,6705,135,1,253586025,80565975,9205245,499590,13860,189,1,
%U A223511 14454403425,4926412575,623675430,39180645,1345050,25578,252,1
%N 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.
%C A223511 Also the Bell transform of A045755(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 29 2016
%e A223511 1;
%e A223511 9,1;
%e A223511 153,27,1;
%e A223511 3825,855,54,1;
%e A223511 126225,32895,2745,90,1;
%e A223511 5175225,1507815,150930,6705,135,1;
%e A223511 253586025,80565975,9205245,499590,13860,189,1;
%e A223511 14454403425,4926412575,623675430,39180645,1345050,25578,252,1;
%p A223511 b[0]:=g(x):
%p A223511 for j from 1 to 10 do
%p A223511 b[j]:=simplify(x^9*diff(b[j-1],x$1);
%p A223511 end do;
%p A223511 # The function BellMatrix is defined in A264428.
%p A223511 # Adds (1,0,0,0, ..) as column 0.
%p A223511 BellMatrix(n -> mul(8*k+1, k=0..n), 10); # _Peter Luschny_, Jan 29 2016
%t A223511 rows = 8;
%t A223511 t = Table[Product[8k+1, {k, 0, n}], {n, 0, rows}];
%t A223511 T[n_, k_] := BellY[n, k, t];
%t A223511 Table[T[n, k], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 22 2018, after _Peter Luschny_ *)
%Y A223511 Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223512-A223522, A223168-A223172, A223523-A223532.
%K A223511 nonn,easy,tabl
%O A223511 1,2
%A A223511 _Udita Katugampola_, Mar 23 2013