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A304330 T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n), triangle read by rows, n >= 0 and 0 <= k <= n. 4
1, 0, 1, 0, 1, 12, 0, 1, 60, 360, 0, 1, 252, 5040, 20160, 0, 1, 1020, 52920, 604800, 1814400, 0, 1, 4092, 506880, 12640320, 99792000, 239500800, 0, 1, 16380, 4684680, 230630400, 3632428800, 21794572800, 43589145600, 0, 1, 65532, 42653520, 3952428480 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..40.

EXAMPLE

Triangle starts:

[0] 1;

[1] 0, 1;

[2] 0, 1,    12;

[3] 0, 1,    60,     360;

[4] 0, 1,   252,    5040,     20160;

[5] 0, 1,  1020,   52920,    604800,    1814400;

[6] 0, 1,  4092,  506880,  12640320,   99792000,   239500800;

[7] 0, 1, 16380, 4684680, 230630400, 3632428800, 21794572800, 43589145600;

MAPLE

T := (n, k) -> add((-1)^j*binomial(2*k, j)*(k-j)^(2*n), j=0..k):

for n from 0 to 8 do seq(T(n, k), k=0..n) od;

CROSSREFS

Row sums are A100872, T(n,2) = A058896, T(n,n) = A002674, T(n,n-1)= A091032.

Cf. A304334, A304336.

Sequence in context: A156401 A246223 A199542 * A322731 A048730 A307163

Adjacent sequences:  A304327 A304328 A304329 * A304331 A304332 A304333

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, May 11 2018

STATUS

approved

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Last modified May 6 05:18 EDT 2021. Contains 343580 sequences. (Running on oeis4.)