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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 Seiichi Manyama, Antidiagonals n = 0..139, flattened 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. Cf. A362043, A362277. Sequence in context: A179067 A061893 A078530 * A336839 A291568 A350559 Adjacent sequences: A362299 A362300 A362301 * A362303 A362304 A362305 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.)