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URL: https://oeis.org/A304334

⇱ A304334 - OEIS

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A304334
T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n)/k!, triangle read by rows, n >= 0 and 0 <= k <= n.
7
1, 0, 1, 0, 1, 6, 0, 1, 30, 60, 0, 1, 126, 840, 840, 0, 1, 510, 8820, 25200, 15120, 0, 1, 2046, 84480, 526680, 831600, 332640, 0, 1, 8190, 780780, 9609600, 30270240, 30270240, 8648640, 0, 1, 32766, 7108920, 164684520, 929728800, 1755673920, 1210809600, 259459200
OFFSET
0,6
FORMULA
T(n, k) = A304330(n, k) / k!.
EXAMPLE
Triangle starts:
[0] 1
[1] 0, 1
[2] 0, 1, 6
[3] 0, 1, 30, 60
[4] 0, 1, 126, 840, 840
[5] 0, 1, 510, 8820, 25200, 15120
[6] 0, 1, 2046, 84480, 526680, 831600, 332640
[7] 0, 1, 8190, 780780, 9609600, 30270240, 30270240, 8648640
[8] 0, 1, 32766, 7108920, 164684520, 929728800, 1755673920, 1210809600, 259459200
MAPLE
A304334 := (n, k) -> add((-1)^j*binomial(2*k, j)*(k-j)^(2*n), j=0..k)/k!:
for n from 0 to 8 do seq(A304334(n, k), k=0..n) od;
PROG
(PARI) T(n, k) = sum(j=0, k, (-1)^j*binomial(2*k, j)*(k - j)^(2*n))/k!;
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 11 2018
CROSSREFS
Row sums are bisection of A081562, T(n,n) ~ A000407, T(n,n-1) ~ A048854(n,2), T(n,2) ~ A002446.
Sequence in context: A352607 A387650 A202185 * A303535 A269340 A388214
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 11 2018
STATUS
approved