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A362302 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/3)} (-k/6)^j * binomial(n-2*j,j)/(n-2*j)!. 7
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, -3, 1, 1, 1, 1, -2, -7, -9, 1, 1, 1, 1, -3, -11, -19, -9, 1, 1, 1, 1, -4, -15, -29, 1, 36, 1, 1, 1, 1, -5, -19, -39, 31, 211, 225, 1, 1, 1, 1, -6, -23, -49, 81, 526, 1009, 477, 1, 1, 1, 1, -7, -27, -59, 151, 981, 2353, 953, -819, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,20
LINKS
FORMULA
E.g.f. of column k: exp(x - k*x^3/6).
T(n,k) = T(n-1,k) - k * binomial(n-1,2) * T(n-3,k) for n > 2.
T(n,k) = n! * Sum_{j=0..floor(n/3)} (-k/6)^j / (j! * (n-3*j)!).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, -5, ...
1, -3, -7, -11, -15, -19, -23, ...
1, -9, -19, -29, -39, -49, -59, ...
1, -9, 1, 31, 81, 151, 241, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n\3, (-k/6)^j/(j!*(n-3*j)!));
CROSSREFS
Columns k=0..2 give A000012, A351929, A362309.
Main diagonal gives A362303.
T(n,2*n) gives A362304.
T(n,6*n) gives A362305.
Sequence in context: A179067 A061893 A078530 * A336839 A291568 A350559
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Apr 15 2023
STATUS
approved

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Last modified February 28 21:38 EST 2024. Contains 370400 sequences. (Running on oeis4.)