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 A176388 A symmetrical triangle:t(n,m)=Floor[(n!/Floor[n/2]!^2)*(Exp[ -(m - n/2)^2/( 2*((n + 1)/4)^2)] - Exp[ -(n/2)^2/(2*((n + 1)/4)^2)]) + 1] 0
 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 3, 5, 3, 1, 1, 11, 21, 21, 11, 1, 1, 6, 13, 16, 13, 6, 1, 1, 34, 76, 106, 106, 76, 34, 1, 1, 15, 33, 50, 56, 50, 33, 15, 1, 1, 112, 258, 402, 493, 493, 402, 258, 112, 1, 1, 40, 91, 146, 188, 204, 188, 146, 91, 40, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The sequence is an approximate adjusted normal probability distribution made integer by the Floor[] operation. Row sums are: {1, 2, 4, 10, 13, 66, 56, 434, 254, 2532, 1136,...}. LINKS Table of n, a(n) for n=0..65. FORMULA t(n,m)=Floor[(n!/Floor[n/2]!^2)*(Exp[ -(m - n/2)^2/( 2*((n + 1)/4)^2)] - Exp[ -(n/2)^2/(2*((n + 1)/4)^2)]) + 1] EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 4, 4, 1}, {1, 3, 5, 3, 1}, {1, 11, 21, 21, 11, 1}, {1, 6, 13, 16, 13, 6, 1}, {1, 34, 76, 106, 106, 76, 34, 1}, {1, 15, 33, 50, 56, 50, 33, 15, 1}, {1, 112, 258, 402, 493, 493, 402, 258, 112, 1}, {1, 40, 91, 146, 188, 204, 188, 146, 91, 40, 1} MATHEMATICA t0[n_, m_] = Floor[(n!/Floor[n/2]!^2)*(Exp[ -(m - n/2)^2/(2*((n + 1)/4)^2)] - Exp[ -(n/2)^2/(2*((n + 1)/4)^2)]) + 1]; Table[Table[t0[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A350912 A055370 A350021 * A282494 A156609 A026637 Adjacent sequences: A176385 A176386 A176387 * A176389 A176390 A176391 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 16 2010 STATUS approved

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Last modified February 29 07:09 EST 2024. Contains 370414 sequences. (Running on oeis4.)