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 A126343 Triangle, read by rows, of the limit of coefficients of q in {[x^m] W(x,q)} as m grows when arranged into a triangle where row n is multiplied by n! for n>=1. 5
 1, 1, 2, 7, 12, 12, 85, 88, 130, 152, 1071, 1140, 1665, 1845, 2430, 16891, 21786, 24501, 32066, 36066, 45222, 363378, 450506, 509110, 631883, 718914, 866306, 991571, 9545369, 10821336, 13004356, 14732096, 17438450, 19851112, 23380260, 26447976 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE The function W that satisfies: W(x,q) = exp( q*x*W(q*x,q) ) begins: W(x,q) = 1 + q*x + (1/2 + q)*q^2*x^2 + (1/6 + 1*q + 1/2*q^2 + 1*q^3)*q^3*x^3 + (1/24 + 1/2*q + 1*q^2 + 7/6*q^3 + 1*q^4 + 1/2*q^5 + 1*q^6)*q^4*x^4 +... Coefficients of q in {[x^n] W(x,q)} tend to a limit when read backwards: n=1: (1/2 + q)*q^2 read backwards: [1, 1/2]; n=2: (1/6 + 1*q + 1/2*q^2 + 1*q^3)*q^3 read backwards: [1, 1/2, 1, 1/6]; n=3: (1/24 + 1/2*q + 1*q^2 + 7/6*q^3 + 1*q^4 + 1/2*q^5 + 1*q^6)*q^4 read backwards: [1, 1/2, 1, 7/6, 1, 1/2, 1/24]. The limit of fractional coefficients may be formed into a triangle: 1, 1/2, 1, 7/6, 2, 2, 85/24, 11/3, 65/12, 19/3, 357/40, 19/2, 111/8, 123/8, 81/4, 16891/720, ... When row n=1,2,3,.. is multiplied by n! we obtain this integer triangle: 1; 1, 2; 7, 12, 12; 85, 88, 130, 152; 1071, 1140, 1665, 1845, 2430; 16891, 21786, 24501, 32066, 36066, 45222; 363378, 450506, 509110, 631883, 718914, 866306, 991571; 9545369, 10821336, 13004356, 14732096, 17438450, 19851112, 23380260, 26447976; 279725995, 316750608, 368695521, 417632601, 484621893, 546334029, 632562585, 713249235, 820357488; 9251279911, 10612100290, 11923578775, 13648746400, 15329052835, 17462968972, 19598497945, 22282099420, 24949824310, 28305482450; ... CROSSREFS Cf. A126341, A126342, A126265; A126344 (column 1), A126345 (diagonal), A126346 (row sums). Sequence in context: A064441 A110949 A226703 * A344951 A174539 A049409 Adjacent sequences:  A126340 A126341 A126342 * A126344 A126345 A126346 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Dec 25 2006 STATUS approved

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Last modified June 14 19:28 EDT 2021. Contains 345038 sequences. (Running on oeis4.)