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 A176990 Table T(n,m) read by rows: the coefficient of [t^n x^m] of 2*n!*(n+2)!*exp(x*t)*( t*(1-exp(t))-exp(t) ) / (1-exp(t) ), 0<=m<=n+1. 0
 2, 4, 13, 6, 6, 0, 104, 24, 16, -2, 0, 780, 120, 60, 0, -48, 0, 6240, 720, 288, 40, 0, -840, 0, 54600, 5040, 1680, 0, 1920, 0, -13440, 0, 524160, 40320, 11520, -3024, 0, 60480, 0, -211680, 0, 5503680, 362880, 90720, 0, -241920, 0, 1612800, 0, -3386880, 0, 62899200, 3628800, 806400, 604800, 0, -11975040, 0, 39916800, 0, -55883520, 0, 778377600, 39916800, 7983360, 0, 72576000, 0, -479001600, 0, 958003200, 0, -958003200, 0, 10378368000, 479001600, 87091200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are: 6, 25, 144, 958, 7200, 60520, 564480, 5803056, 65318400, 798940800, 10538035200,.... The bivariate expansion is exp(x*t)*( t*(1-exp(t))-exp(t) )/ (1-exp(t) )= 1/t +(1/2+x)*t^0 + (13/12+x/2+x^2/2)*t +... The leading term 1/t corresponding to n = -1 is dropped, and the other rows are scaled with a factor 2*n!*(n+2)!. LINKS Table of n, a(n) for n=0..76. EXAMPLE 2, 4; 13, 6, 6; 0, 104, 24, 16; -2, 0, 780, 120, 60; 0, -48, 0, 6240, 720, 288; 40, 0, -840, 0, 54600, 5040, 1680; 0,1920, 0, -13440, 0, 524160, 40320, 11520; -3024, 0, 60480, 0, -211680, 0, 5503680, 362880, 90720; 0, -241920, 0, 1612800, 0, -3386880, 0, 62899200, 3628800, 806400; 604800, 0, -11975040, 0, 39916800, 0, -55883520, 0, 778377600, 39916800, 7983360; 0,72576000, 0, -479001600, 0, 958003200, 0, -958003200, 0, 10378368000, 479001600, 87091200; MATHEMATICA p[t_] = Exp[x*t](t*(1 - Exp[t]) - Exp[t])/(1 - Exp[t]); a = Table[ CoefficientList[(n!*(n + 2)!*2)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Cf. A176989. Sequence in context: A030064 A224886 A180500 * A109928 A023640 A064454 Adjacent sequences: A176987 A176988 A176989 * A176991 A176992 A176993 KEYWORD sign,tabf AUTHOR Roger L. Bagula, Dec 08 2010 STATUS approved

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Last modified June 5 02:01 EDT 2023. Contains 363130 sequences. (Running on oeis4.)