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 A006199 Bessel polynomial {y_n}'(-1). (Formerly M3082) 4
 0, 1, -3, 21, -185, 2010, -25914, 386407, -6539679, 123823305, -2593076255, 59505341676, -1484818160748, 40025880386401, -1159156815431055, 35891098374564105, -1183172853341759129, 41372997479943753582, -1529550505546305534414, 59608871544962952539335 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Absolute values give partitions into pairs. REFERENCES G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonné, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74. J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 1..400 FORMULA a(n) = A000806(n) + (n-1) * A000806(n-1). - Sean A. Irvine, Jan 23 2017 From G. C. Greubel, Aug 14 2017: (Start) a(n) = 2*n*(1/2)_{n} * (-2)^(n-1) * hyergeometric1f1(1-n; -2*n; -2), where (a)_{n} is the Pochhammer symbol. E.g.f.: (1+2*x)^(-3/2)*( (1+2*x)^(3/2) - x*(1+2*x)^(1/2) - x -1) * exp(sqrt(1+2*x) - 1), for offset 0. (End) G.f.: (x/(1-x)^3)*hypergeometric2f0(2,3/2; - ; -2*x/(1-x)^2), for offset 0. - G. C. Greubel, Aug 16 2017 MATHEMATICA Join[{0}, Table[2*n*Pochhammer[1/2, n]*(-2)^(n - 1)* Hypergeometric1F1[1 - n, -2*n, -2], {n, 1, 50}]] (* G. C. Greubel, Aug 14 2017 *) PROG (PARI) for(n=0, 50, print1(sum(k=0, n-1, ((n+k)!/(k!*(n-k)!))*(-1/2)^k), ", ")) \\ G. C. Greubel, Aug 14 2017 CROSSREFS Cf. A000806, A001514, A065707, A065920, A065921, A065922. Sequence in context: A054879 A333090 A131763 * A083063 A012163 A012055 Adjacent sequences:  A006196 A006197 A006198 * A006200 A006201 A006202 KEYWORD sign AUTHOR STATUS approved

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Last modified July 2 16:36 EDT 2022. Contains 355029 sequences. (Running on oeis4.)