A253667 - OEIS

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A253667

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

1, 1, -1, 1, 0, 1, 1, 1, -1, -1, 1, 2, -1, 2, 1, 1, 3, 1, -1, -3, -1, 1, 4, 5, -4, 5, 4, 1, 1, 5, 11, -1, 1, -11, -5, -1, 1, 6, 19, 14, -15, 14, 19, 6, 1, 1, 7, 29, 47, -19, 19, -47, -29, -7, -1, 1, 8, 41, 104, 37, -56, 37, 104, 41, 8, 1

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

OFFSET

0,12

LINKS

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

FORMULA

T(n,n) = A009940(n).

EXAMPLE

Square array starts:

[n\k][0 1 2 3 4 5 6]

[0] 1, -1, 1, -1, 1, -1, 1, ...

[1] 1, 0, -1, 2, -3, 4, -5, ...

[2] 1, 1, -1, -1, 5, -11, 19, ...

[3] 1, 2, 1, -4, 1, 14, -47, ...

[4] 1, 3, 5, -1, -15, 19, 37, ...

[5] 1, 4, 11, 14, -19, -56, 151, ...

[6] 1, 5, 19, 47, 37, -151, -185, ...

The first few rows as a triangle:

1, -1,

1, 0, 1,

1, 1, -1, -1,

1, 2, -1, 2, 1,

1, 3, 1, -1, -3, -1,

1, 4, 5, -4, 5, 4, 1.

MAPLE

T := (n, k) -> k!*coeff(series(exp(-x)*add(binomial(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. A009940.

Sequence in context: A261095 A249809 A075104 * A360189 A368210 A233932

Adjacent sequences: A253664 A253665 A253666 * A253668 A253669 A253670

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Jan 18 2015

STATUS

approved