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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. 24
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also the Bell transform of A045755(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016
LINKS
EXAMPLE
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;
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 *)
CROSSREFS
Sequence in context: A113394 A243754 A254932 * A051231 A258437 A046761
KEYWORD
nonn,easy,tabl
AUTHOR
Udita Katugampola, Mar 23 2013
STATUS
approved

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Last modified May 19 20:38 EDT 2024. Contains 372703 sequences. (Running on oeis4.)