A253670 Square array read by ascending antidiagonals, T(n, k) = k!*[x^k](exp(x)*sum(j=0..n, C(2*n,j)*x^j)), n>=0, k>=0.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 21, 7, 1, 1, 9, 43, 49, 9, 1, 1, 11, 73, 229, 89, 11, 1, 1, 13, 111, 529, 685, 141, 13, 1, 1, 15, 157, 1021, 3393, 1531, 205, 15, 1, 1, 17, 211, 1753, 8501, 12361, 2887, 281, 17, 1, 1, 19, 273, 2773, 18001, 63591, 32809, 4873, 369, 19, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

T(n,n) = A082545(n).

Example

Square array starts:
[n\k][0   1    2     3      4       5        6]
[0]   1,  1,   1,    1,     1,      1,       1, ...
[1]   1,  3,   5,    7,     9,     11,      13, ...
[2]   1,  5,  21,   49,    89,    141,     205, ...
[3]   1,  7,  43,  229,   685,   1531,    2887, ...
[4]   1,  9,  73,  529,  3393,  12361,   32809, ...
[5]   1, 11, 111, 1021,  8501,  63591,  272851, ...
[6]   1, 13, 157, 1753, 18001, 169021, 1442173, ...
The first few rows as a triangle:
1
1,  1
1,  3,  1
1,  5,  5,   1
1,  7, 21,   7,  1
1,  9, 43,  49,  9,  1
1, 11, 73, 229, 89, 11, 1

Maple

T := (n, k) -> k!*coeff(series(exp(x)*add(binomial(2*n, j)*x^j, j=0..n), x, k+1), x, k): for n from 0 to 6 do lprint(seq(T(n, k), k=0..6)) od;

Crossrefs

Cf. A082545.

Sequence in context: A086620 A338934 A228356 * A137897 A296327 A347970

Adjacent sequences: A253667 A253668 A253669 * A253671 A253672 A253673

Keyword

nonn,tabl

Author

Peter Luschny, Jan 18 2015

Status

approved