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A318260 Generalized Worpitzky numbers W_{m}(n,k) for m = 3, n >= 0 and 0 <= k <= n, triangle read by rows. 1
1, -1, 1, 19, -39, 20, -1513, 4705, -4872, 1680, 315523, -1314807, 2052644, -1422960, 369600, -136085041, 710968441, -1484552160, 1548707160, -807206400, 168168000, 105261234643, -661231439271, 1729495989332, -2410936679424, 1889230062720, -789044256000, 137225088000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The triangle can be seen as a member of a family of generalized Worpitzky numbers A028246. See A318259 and the cross-references for some other members.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

Let P(m,n) = Sum_{k=1..n} binomial(m*n, m*k)*P(m, n-k)*x with P(m,0) = 1

and S(n,k) = [x^k]P(3,n), then T(n,k) = Sum_{j=0..k}((-1)^(k-j)*binomial(n-j, n-k)* Sum_{i=0..n}((-1)^i*S(n,i)*binomial(n-i,j))).

EXAMPLE

[0] [         1]

[1] [        -1,         1]

[2] [        19,       -39,          20]

[3] [     -1513,      4705,       -4872,       1680]

[4] [    315523,  -1314807,     2052644,   -1422960,     369600]

[5] [-136085041, 710968441, -1484552160, 1548707160, -807206400, 168168000]

PROG

(Sage)

# Function EW id defined in A318259.

def A318260row(n): return EW(3, n)

print flatten([A318260row(n) for n in (0..6)])

CROSSREFS

Cf. T(n,0) ~ A002115(n) (signed), T(n,n) = A014606.

Cf. A167374 (m=0), A028246 & A163626 (m=1), A318259 (m=2), this seq (m=3).

Sequence in context: A008601 A033900 A110288 * A050813 A041712 A041710

Adjacent sequences:  A318257 A318258 A318259 * A318261 A318262 A318263

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Sep 06 2018

STATUS

approved

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Last modified April 26 08:14 EDT 2019. Contains 322472 sequences. (Running on oeis4.)