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 A171631 Triangle read by rows: T(n,k) = n*(binomial(n-2, k-1) + n*binomial(n-2, k)), n > 0 and 0 <= k <= n - 1. 1
 1, 4, 2, 9, 12, 3, 16, 36, 24, 4, 25, 80, 90, 40, 5, 36, 150, 240, 180, 60, 6, 49, 252, 525, 560, 315, 84, 7, 64, 392, 1008, 1400, 1120, 504, 112, 8, 81, 576, 1764, 3024, 3150, 2016, 756, 144, 9, 100, 810, 2880, 5880, 7560, 6300, 3360, 1080, 180, 10, 121, 1100 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If T(0,0) = 0 is prepended, then row sums give A001788. REFERENCES Eugene Jahnke and Fritz Emde, Table of Functions with Formulae and Curves, Dover Publications, 1945, p. 32. LINKS Table of n, a(n) for n=1..57. FORMULA Let p(x;n) = (x + 1)^n. Then row n are the coefficients in the expansion of p''(x;n) - x*p'(x;n) + n*p(x;n) = n*(x + n)*(x + 1)^(n - 2). From Franck Maminirina Ramaharo, Oct 02 2018: (Start) T(n,1) = A000290(n). T(n,2) = A011379(n). T(n,3) = 3*A002417(n-2). T(n,n-2) = A046092(n-1). T(n,n-3) = 9*A000292(n-2). G.f.: y*(x*y - y - 1)/(x*y + y - 1)^3. (End) EXAMPLE Triangle begins: n\k| 0 1 2 3 4 6 7 8 9 ------------------------------------------------- 1 | 1 2 | 4 2 3 | 9 12 3 4 | 16 36 24 4 5 | 25 80 90 40 5 6 | 36 150 240 180 60 6 7 | 49 252 525 560 315 84 7 8 | 64 392 1008 1400 1120 504 112 8 9 | 81 576 1764 3024 3150 2016 756 144 9 ... reformatted. - Franck Maminirina Ramaharo, Oct 02 2018 MATHEMATICA Table[CoefficientList[n*(x + n)*(x + 1)^(n - 2), x], {n, 1, 12}]//Flatten PROG (Maxima) T(n, k) := n*(binomial(n - 2, k - 1) + n*binomial(n - 2, k))\$ tabl(nn) := for n:1 thru nn do print(makelist(T(n, k), k, 0, n - 1))\$ /* Franck Maminirina Ramaharo, Oct 02 2018 */ CROSSREFS Cf. A003506, A007318, A127952, A171531. Sequence in context: A233295 A298567 A006172 * A052915 A130273 A016516 Adjacent sequences: A171628 A171629 A171630 * A171632 A171633 A171634 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Dec 13 2009 EXTENSIONS Edited and new name by Franck Maminirina Ramaharo, Oct 02 2018 STATUS approved

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Last modified September 7 07:38 EDT 2024. Contains 375729 sequences. (Running on oeis4.)