A357340 - OEIS

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A357340

Triangle read by rows. T(n, k) = Sum_{j=0..n-k} binomial(-n, j) * A268438(n - k, j).

1, -1, 1, 2, -2, 1, 0, 12, -3, 1, -56, -120, 28, -4, 1, 0, 1680, -450, 50, -5, 1, 15840, -30240, 10416, -1080, 78, -6, 1, 0, 665280, -317520, 33712, -2100, 112, -7, 1, -17297280, -17297280, 12070080, -1391040, 81648, -3600, 152, -8, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

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

EXAMPLE

Triangle T(n, k) starts:

[0] 1;

[1] -1, 1;

[2] 2, -2, 1;

[3] 0, 12, -3, 1;

[4] -56, -120, 28, -4, 1;

[5] 0, 1680, -450, 50, -5, 1;

[6] 15840, -30240, 10416, -1080, 78, -6, 1;

[7] 0, 665280, -317520, 33712, -2100, 112, -7, 1;

[8] -17297280, -17297280, 12070080, -1391040, 81648, -3600, 152, -8, 1;

MAPLE

A357340 := proc(n, k) local u; u := n - k; (2*u)!*add(binomial(-n, j) * j! *

add((-1)^(j+m)*binomial(u+j, u+m)*abs(Stirling1(u+m, m)), m=0..j)/(u +j)!, j=0..u) end: seq(print(seq(A357340(n, k), k=0..n)), n=0..8);

PROG

(SageMath) # using function A268438

def A357340(n, k):

return sum(binomial(-n, i) * A268438(n - k, i) for i in range(n - k + 1))

for n in range(10): print([A357340(n, k) for k in range(n + 1)])

CROSSREFS

Cf. A357341 (alternating row sums), A264437, A268438, A357339.

Sequence in context: A360604 A266318 A011265 * A356818 A265863 A083747

Adjacent sequences: A357337 A357338 A357339 * A357341 A357342 A357343

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Sep 25 2022

STATUS

approved