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 A254286 Expansion of (1 - (1-256*x)^(1/4)) / (64*x). 5
 1, 96, 14336, 2523136, 484442112, 98180268032, 20645907791872, 4459516083044352, 983075545417777152, 220208922173582082048, 49967406340478261526528, 11459191854083014643417088, 2651480699775516003646046208, 618173786004806016850049630208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..250 FORMULA G.f.: (1 - (1-256*x)^(1/4)) / (64*x). a(n) ~ 256^n / (Gamma(3/4) * n^(5/4)). Recurrence: (n+1)*a(n) = 64*(4*n-1)*a(n-1). a(n) = 256^n * Gamma(n+3/4) / (Gamma(3/4) * Gamma(n+2)). E.g.f.: hypergeom([3/4], [2], 256*x). - Vaclav Kotesovec, Jan 28 2015 From Peter Bala, Sep 01 2017: (Start) a(n) = (-1)^n*binomial(1/4, n+1)*4^(4*n+1). Cf. A000108(n) = (-1)^n*binomial(1/2, n+1)*2^(2*n+1). a(n) = 16^n*A025749(n+1); a(n) = 32^n*A048779(n+1). (End) MAPLE a:=series((1-(1-256*x)^(1/4))/(64*x), x=0, 14): seq(coeff(a, x, n), n=0..13); # Paolo P. Lava, Mar 27 2019 MATHEMATICA CoefficientList[Series[(1-(1-256*x)^(1/4)) / (64*x), {x, 0, 20}], x] CoefficientList[Series[Hypergeometric1F1[3/4, 2, 256*x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2015 *) PROG (Magma) [Round(2^(8*n)*Gamma(n+3/4)/(Gamma(3/4)*Gamma(n+2))): n in [0..30]]; // G. C. Greubel, Aug 10 2022 (SageMath) [2^(8*n)*rising_factorial(3/4, n)/factorial(n+1) for n in (0..30)] # G. C. Greubel, Aug 10 2022 CROSSREFS Cf. A000108, A008545, A025749, A048779, A254282, A254287. Sequence in context: A189909 A189903 A189159 * A216039 A208443 A183418 Adjacent sequences: A254283 A254284 A254285 * A254287 A254288 A254289 KEYWORD nonn,easy AUTHOR Vaclav Kotesovec, Jan 27 2015 STATUS approved

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Last modified December 5 08:36 EST 2022. Contains 358585 sequences. (Running on oeis4.)