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 A275324 Expansion of (x*(1-4*x^2)^(-3/2) + (1-4*x^2)^(-1/2) + x + 1)/2. 2
 1, 1, 1, 3, 3, 15, 10, 70, 35, 315, 126, 1386, 462, 6006, 1716, 25740, 6435, 109395, 24310, 461890, 92378, 1939938, 352716, 8112468, 1352078, 33801950, 5200300, 140408100, 20058300, 581690700, 77558760, 2404321560, 300540195, 9917826435, 1166803110, 40838108850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA Interweaved from (1+(1-4*x)^(-1/2))/2 (compare A088218 & A001700) and (1+(1-4*x)^(-3/2))/2 (compare A033876). E.g.f.: (1 + x)*(1 + BesselI(0, 2*x))/2. For a recurrence see the Sage script. a(n) = A056040(n)/2 for n>=2. MAPLE st := (x*(1-4*x^2)^(-3/2)+(1-4*x^2)^(-1/2)+x+1)/2: series(st, x, 36): PolynomialTools:-CoefficientList(convert(%, polynom), x); MATHEMATICA Table[If[n<2, 1, n!/Quotient[n, 2]!^2/2], {n, 0, 30}] CoefficientList[Series[(x*(1 - 4*x^2)^(-3/2) + (1 - 4*x^2)^(-1/2) + x + 1)/2, {x, 0, 50}], x] (* G. C. Greubel, Aug 15 2016 *) PROG (Sage) def A275324():     r, n = 2, 1     yield 1     yield 1     while True:         n += 1         r *= 4/n if is_even(n) else n         yield r // 4 a = A275324(); print [a.next() for i in range(16)] CROSSREFS Cf. A001700, A033876, A088218, A056040. Sequence in context: A285562 A285542 A160612 * A282663 A282124 A281421 Adjacent sequences:  A275321 A275322 A275323 * A275325 A275326 A275327 KEYWORD nonn AUTHOR Peter Luschny, Aug 15 2016 STATUS approved

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Last modified July 17 21:36 EDT 2019. Contains 325109 sequences. (Running on oeis4.)