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 A144446 Array t(n, k) = (k*(n-1) +2-k)*t(n-1, k) + k*t(n-2, k), with t(1, k) = 1, t(2, k) = 2, read by antidiagonals. 2
 1, 2, 1, 7, 2, 1, 30, 10, 2, 1, 157, 64, 13, 2, 1, 972, 532, 110, 16, 2, 1, 6961, 5448, 1249, 168, 19, 2, 1, 56660, 66440, 17816, 2416, 238, 22, 2, 1, 516901, 941056, 306619, 44160, 4141, 320, 25, 2, 1, 5225670, 15189776, 6185828, 981184, 92292, 6532, 414, 28, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Antidiagonals n = 1..50, flattened FORMULA T(n, k) = t(n-k+1, k), where t(n, k) = (k*(n-1) +2-k)*t(n-1, k) + k*t(n-2, k) with t(1, k) = 1, t(2, k) = 2. T(n, 1) = A001053(n+1). T(n, k) = (k*(n-k)+2-k)*T(n-1, k) + k*T(n-2, k) with T(n, n-1) = 2, T(n, n) = 1 (as a triangle). - G. C. Greubel, Mar 05 2022 EXAMPLE Array t(n,k) begins as: 1, 1, 1, 1, 1, 1, ...; 2, 2, 2, 2, 2, 2, ...; 7, 10, 13, 16, 19, 22, ...; 30, 64, 110, 168, 238, 320, ...; 157, 532, 1249, 2416, 4141, 6532, ...; 972, 5448, 17816, 44160, 92292, 171752, ...; Antidiagonal triangle T(n,k) begins as: 1; 2, 1; 7, 2, 1; 30, 10, 2, 1; 157, 64, 13, 2, 1; 972, 532, 110, 16, 2, 1; 6961, 5448, 1249, 168, 19, 2, 1; 56660, 66440, 17816, 2416, 238, 22, 2, 1; 516901, 941056, 306619, 44160, 4141, 320, 25, 2, 1; 5225670, 15189776, 6185828, 981184, 92292, 6532, 414, 28, 2, 1; MATHEMATICA t[n_, k_]:= t[n, k]= If[n<3, n, (k*(n-1) +2-k)*t[n-1, k] + k*t[n-2, k]]; T[n_, k_]:= t[n-k+1, k]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Mar 05 2022 *) PROG (Magma) function T(n, k) // triangle form; A144446 if k gt n-2 then return n-k+1; else return (k*(n-k)+2-k)*T(n-1, k) + k*T(n-2, k); end if; return T; end function; [T(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 05 2022 (Sage) def t(n, k): return n if(n<3) else (k*(n-1) +2-k)*t(n-1, k) + k*t(n-2, k) def A144446(n, k): return t(n-k+1, k) flatten([[A144446(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 05 2022 CROSSREFS Cf. A144431, A144432, A144435, A144436, A144438, A144439, A144440, A144441, A144442, A144443, A144444, A144445, A144447. Cf. A001053. Sequence in context: A128747 A205945 A124392 * A121416 A317547 A089329 Adjacent sequences: A144443 A144444 A144445 * A144447 A144448 A144449 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 05 2008 EXTENSIONS Edited by G. C. Greubel, Mar 05 2022 STATUS approved

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Last modified June 10 02:46 EDT 2023. Contains 363183 sequences. (Running on oeis4.)