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

0,6

LINKS

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

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.

Cf. A304330, A304334.

Sequence in context: A277410 A289546 A279031 * A287315 A256311 A022695

Adjacent sequences:  A304333 A304334 A304335 * A304337 A304338 A304339

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, May 11 2018

STATUS

approved

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)