login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
24

%I #14 Jun 22 2018 09:22:47

%S 1,9,1,153,27,1,3825,855,54,1,126225,32895,2745,90,1,5175225,1507815,

%T 150930,6705,135,1,253586025,80565975,9205245,499590,13860,189,1,

%U 14454403425,4926412575,623675430,39180645,1345050,25578,252,1

%N 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 Also the Bell transform of A045755(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 29 2016

%e 1;

%e 9,1;

%e 153,27,1;

%e 3825,855,54,1;

%e 126225,32895,2745,90,1;

%e 5175225,1507815,150930,6705,135,1;

%e 253586025,80565975,9205245,499590,13860,189,1;

%e 14454403425,4926412575,623675430,39180645,1345050,25578,252,1;

%p b[0]:=g(x):

%p for j from 1 to 10 do

%p b[j]:=simplify(x^9*diff(b[j-1],x$1);

%p end do;

%p # The function BellMatrix is defined in A264428.

%p # Adds (1,0,0,0, ..) as column 0.

%p BellMatrix(n -> mul(8*k+1, k=0..n), 10); # _Peter Luschny_, Jan 29 2016

%t rows = 8;

%t t = Table[Product[8k+1, {k, 0, n}], {n, 0, rows}];

%t T[n_, k_] := BellY[n, k, t];

%t Table[T[n, k], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 22 2018, after _Peter Luschny_ *)

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

%K nonn,easy,tabl

%O 1,2

%A _Udita Katugampola_, Mar 23 2013