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 A073278 A triangle constructed from the coefficients of the n-th derivative of the normal probability distribution function. 1
 1, -1, 0, 1, 0, -1, -1, 0, 3, 0, 1, 0, -6, 0, 3, -1, 0, 10, 0, -15, 0, 1, 0, -15, 0, 45, 0, -15, -1, 0, 21, 0, -105, 0, 105, 0, 1, 0, -28, 0, 210, 0, -420, 0, 105, -1, 0, 36, 0, -378, 0, 1260, 0, -945, 0, 1, 0, -45, 0, 630, 0, -3150, 0, 4725, 0, -945, -1, 0, 55, 0, -990, 0, 6930, 0, -17325, 0, 10395, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS The n-th derivative of the normal probability distribution function will be a polynomial of n degrees times f(x) of which every other term is zero. All coefficients are triangular numbers. The second nonzero diagonal are the triangular numbers (A000217), the third nonzero diagonal are the tritriangular numbers (A050534), etc. REFERENCES Samuel M. Selby, Editor-in-Chief, CRC Standard Mathematical Tables, 21st Edition, 1973, pp. 582. LINKS FORMULA a(n) = the coefficient list of the x's of the n-th d(e^(-x^2 /2)/dx. EXAMPLE f(x) = 1/Sqrt(2*Pi) * e^(-x^2 /2). The polynomial involved in the seventh derivative of the f(x)/dx is (x^7 + 21x^5 - 105x^3 + 105x). Therefore the seventh antidiagonal reads the coefficients as 1, 0, 21, 0, -105, 0, 105. 1; 1,0; 1,0,1; 1,0,3,0; ... MATHEMATICA y = E^(-x^2/2); Flatten[ Table[ Reverse[ CoefficientList[ Dt[y, {x, n}]/y, x]], {n, 0, 11} ]] CROSSREFS Sequence in context: A056100 A141665 A136689 * A081658 A187253 A022904 Adjacent sequences:  A073275 A073276 A073277 * A073279 A073280 A073281 KEYWORD sign AUTHOR Robert G. Wilson v, Jul 23 2002 STATUS approved

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)