A341200 - OEIS

A341200

Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} j^k * (n-j)! * binomial(n,j)^2.

1, 0, 2, 0, 1, 7, 0, 1, 6, 34, 0, 1, 8, 39, 209, 0, 1, 12, 63, 292, 1546, 0, 1, 20, 117, 544, 2505, 13327, 0, 1, 36, 243, 1168, 5225, 24306, 130922, 0, 1, 68, 549, 2800, 12525, 55656, 263431, 1441729, 0, 1, 132, 1323, 7312, 33425, 145836, 653023, 3154824, 17572114

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..54.

FORMULA

About e.g.f. of column k, see A105218 or A105219 comment.

EXAMPLE

Square array begins:

1, 0, 0, 0, 0, 0, ...

2, 1, 1, 1, 1, 1, ...

7, 6, 8, 12, 20, 36, ...

34, 39, 63, 117, 243, 549, ...

209, 292, 544, 1168, 2800, 7312, ...

1546, 2505, 5225, 12525, 33425, 97125, ...

MATHEMATICA

T[n_, k_] := Sum[If[j == k == 0, 1, j^k] * (n - j)! * Binomial[n, j]^2, {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 06 2021 *)

PROG

(PARI) T(n, k) = sum(j=0, n, j^k*(n-j)!*binomial(n, j)^2);

CROSSREFS

Columns k=0..4 gives A002720, A103194, A105219, A105218, A341196.

Main diagonal gives A341197.

Cf. A289192.

Sequence in context: A367073 A176129 A362787 * A300130 A101371 A325754

Adjacent sequences: A341197 A341198 A341199 * A341201 A341202 A341203

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Feb 06 2021

STATUS

approved