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A328748 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is Sum_{i=0..n} (-2)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^k. 7
1, 1, 0, 1, 0, -1, 1, 0, 0, 2, 1, 0, 2, 0, -3, 1, 0, 6, 0, 0, 4, 1, 0, 14, 12, 6, 0, -5, 1, 0, 30, 72, 90, 0, 0, 6, 1, 0, 62, 300, 882, 360, 20, 0, -7, 1, 0, 126, 1080, 6690, 8400, 2040, 0, 0, 8, 1, 0, 254, 3612, 44706, 124920, 95180, 10080, 70, 0, -9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

T(n,k) is the constant term in the expansion of (-2 + Product_{j=1..k-1} (1 + x_j) + Product_{j=1..k-1} (1 + 1/x_j))^n for k > 0.

LINKS

Seiichi Manyama, Antidiagonals n = 0..100, flattened

EXAMPLE

Square array begins:

    1, 1, 1,   1,    1,      1, ...

    0, 0, 0,   0,    0,      0, ...

   -1, 0, 2,   6,   14,     30, ...

    2, 0, 0,  12,   72,    300, ...

   -3, 0, 6,  90,  882,   6690, ...

    4, 0, 0, 360, 8400, 124920, ...

CROSSREFS

Columns k=0..5 give A097141(n+1), A000007, A126869, A002898, A328735, A328751.

T(n,n+1) gives A328814.

Cf. A309010, A328747, A328807.

Sequence in context: A320836 A097567 A022881 * A093201 A067613 A264034

Adjacent sequences:  A328745 A328746 A328747 * A328749 A328750 A328751

KEYWORD

sign,tabl

AUTHOR

Seiichi Manyama, Oct 27 2019

STATUS

approved

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Last modified April 15 10:45 EDT 2021. Contains 342977 sequences. (Running on oeis4.)