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A304336
T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n)/(k!)^2, triangle read by rows, n >= 0 and 0 <= k <= n.
5
1, 0, 1, 0, 1, 3, 0, 1, 15, 10, 0, 1, 63, 140, 35, 0, 1, 255, 1470, 1050, 126, 0, 1, 1023, 14080, 21945, 6930, 462, 0, 1, 4095, 130130, 400400, 252252, 42042, 1716, 0, 1, 16383, 1184820, 6861855, 7747740, 2438436, 240240, 6435
OFFSET
0,6
FORMULA
T(n, k) = A304330(n, k)/(k!)^2.
T(n, k) = A304334(n, k)/k!.
EXAMPLE
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 1, 3;
[3] 0, 1, 15, 10;
[4] 0, 1, 63, 140, 35;
[5] 0, 1, 255, 1470, 1050, 126;
[6] 0, 1, 1023, 14080, 21945, 6930, 462;
[7] 0, 1, 4095, 130130, 400400, 252252, 42042, 1716;
[8] 0, 1, 16383, 1184820, 6861855, 7747740, 2438436, 240240, 6435;
MAPLE
A304336 := (n, k) -> add((-1)^j*binomial(2*k, j)*(k-j)^(2*n), j=0..k)/(k!)^2:
for n from 0 to 8 do seq(A304336(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!)^2;
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 11 2018
CROSSREFS
Row sums are A304338, T(n,n) = A088218 and A001700, T(n,n-1) ~ A002803, T(n,2) ~ A024036, T(n,3) ~ bisection of A174395.
Sequence in context: A289546 A334823 A279031 * A287315 A350212 A256311
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 11 2018
STATUS
approved