A364661 Numerators of coefficients in expansion of (1 + x)^(3/4).
1, 3, -3, 5, -45, 117, -663, 1989, -49725, 160225, -1057485, 3556995, -48612265, 168273225, -1177912575, 4161957765, -237231592605, 851242773465, -6147864475025, 22326455198775, -325966245902115, 1195209568307755, -8801088639357105, 32525762362841475, -964930950097630425
Offset: 0
Examples
(1 + x)^(3/4) = 1 + 3*x/4 - 3*x^2/32 + 5*x^3/128 - 45*x^4/2048 + 117*x^5/8192 - 663*x^6/65536 + ... Coefficients are 1, 3/4, -3/32, 5/128, -45/2048, 117/8192, -663/65536, ...
Programs
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Mathematica
nmax = 24; CoefficientList[Series[(1 + x)^(3/4), {x, 0, nmax}], x] // Numerator Table[Binomial[3/4, n], {n, 0, 24}] // Numerator -
PARI
my(x='x+O('x^30)); apply(numerator, Vec((1 + x)^(3/4))) \\ Michel Marcus, Aug 02 2023