A357339 Triangle read by rows. T(n, k) = Sum_{j=0..n-k} binomial(-n, j) * A268437(n - k, j).

1, -1, 1, 10, -2, 1, -270, 24, -3, 1, 14056, -720, 44, -4, 1, -1197000, 40320, -1500, 70, -5, 1, 151169040, -3628800, 92064, -2700, 102, -6, 1, -26521775280, 479001600, -8890560, 181888, -4410, 140, -7, 1, 6169461217920, -87178291200, 1241982720, -18910080, 324912, -6720, 184, -8, 1

Offset

0,4

Links

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

Example

Triangle starts:
[0]         1;
[1]        -1,        1;
[2]        10,       -2,     1;
[3]      -270,       24,    -3,     1;
[4]     14056,     -720,    44,    -4,   1;
[5]  -1197000,    40320, -1500,    70,  -5,  1;
[6] 151169040, -3628800, 92064, -2700, 102, -6, 1;

Maple

A357339 := proc(n, k) local u; u:=(n - k); (2*u)!*add(binomial(-n, j) * j! * add((-1)^(j+m)*binomial(u+j, u+m)*Stirling2(u+m, m), m=0..j) / (u+j)!, j=0..u) end: seq(print(seq(A357339(n, k), k=0..n)), n=0..6);

Prog

(SageMath) # using function A268437.
def A357339(n, k):
    return sum(binomial(-n, i) * A268437(n - k, i) for i in range(n - k + 1))
for n in range(9): print([A357339(n, k) for k in range(n + 1)])

Crossrefs

Cf. A357342 (alternating row sums), A268437, A357340.

Sequence in context: A010174 A073755 A010173 * A259712 A343103 A136712

Adjacent sequences: A357336 A357337 A357338 * A357340 A357341 A357342

Keyword

sign,tabl

Author

Peter Luschny, Sep 25 2022

Status

approved