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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.
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
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
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 18 2015
STATUS
approved