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

1,2

Comments

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

Links

Table of n, a(n) for n=1..36.

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

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

Sequence in context: A113394 A243754 A254932 * A051231 A258437 A046761

Adjacent sequences: A223508 A223509 A223510 * A223512 A223513 A223514

Keyword

nonn,easy,tabl

Author

Udita Katugampola, Mar 23 2013

Status

approved