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A333142 Triangle read by rows: T(n, k) = qStirling1(n, k, q) for q = 2, with 0 <= k <= n. 2
1, 1, 1, 1, 2, 1, 1, 7, 5, 1, 1, 50, 42, 12, 1, 1, 751, 680, 222, 27, 1, 1, 23282, 21831, 7562, 1059, 58, 1, 1, 1466767, 1398635, 498237, 74279, 4713, 121, 1, 1, 186279410, 179093412, 64674734, 9931670, 672830, 20080, 248, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..44.

FORMULA

qStirling1(n, k, q) = qStirling1(n-1, k-1, q) + qBrackets(n-1, q)*qStirling1(n-1, k, q) with boundary values 0^k if n = 0 and n^0 if k = 0.

Note that also a second definition is used in the literature. The two versions differ by a factor of q^(n-k).

EXAMPLE

Triangle starts:

[0] 1

[1] 1, 1

[2] 1, 2, 1

[3] 1, 7, 5, 1

[4] 1, 50, 42, 12, 1

[5] 1, 751, 680, 222, 27, 1

[6] 1, 23282, 21831, 7562, 1059, 58, 1

[7] 1, 1466767, 1398635, 498237, 74279, 4713, 121, 1

[8] 1, 186279410, 179093412, 64674734, 9931670, 672830, 20080, 248, 1

MAPLE

qStirling1 := proc(n, k, q) option remember; with(QDifferenceEquations):

if n = 0 then return 0^k fi; if k = 0 then return n^0 fi;

qStirling1(n-1, k-1, p) + QBrackets(n-1, p)*qStirling1(n-1, k, p);

subs(p = q, expand(%)) end:

seq(seq(qStirling1(n, k, 2), k=0..n), n=0..9);

CROSSREFS

T(n,n-1) = A000325(n).

Cf. A333143.

Sequence in context: A143670 A169730 A220725 * A196832 A005450 A039760

Adjacent sequences: A333139 A333140 A333141 * A333143 A333144 A333145

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Mar 09 2020

STATUS

approved

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Last modified November 27 06:50 EST 2022. Contains 358362 sequences. (Running on oeis4.)