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 A101055 E.g.f.: exp(exp(x)-1)/(1-x)^3. 1
 1, 4, 20, 119, 819, 6397, 55919, 541144, 5746596, 66475311, 832418065, 11222752125, 162133146877, 2499401777680, 40960858008040, 711240364356155, 13045720176453587, 252079975222183461, 5118581045978055067, 108972887981432267708, 2427417968714846394712, 56467770394205361146187 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence appears in the problem of normal ordering of functions of boson operators. LINKS FORMULA a(n) = ((-1)^n*n!/e)*Sum_{k>=0} L(n,-n-3,k)/k!, where L is a generalized Laguerre polynomial. a(n) = (1/2)*Sum_{k=0..n} binomial(n,k)*(k + 2)!*Bell(n-k), where Bell() = A000110. - Ilya Gutkovskiy, May 24 2018 CROSSREFS Cf. A000110, A101053, A101054. Sequence in context: A258666 A128236 A091046 * A208232 A013197 A319788 Adjacent sequences:  A101052 A101053 A101054 * A101056 A101057 A101058 KEYWORD nonn AUTHOR Karol A. Penson, Nov 29 2004 EXTENSIONS Terms after a(15) from Ilya Gutkovskiy, May 24 2018 STATUS approved

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Last modified December 7 03:27 EST 2019. Contains 329836 sequences. (Running on oeis4.)