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

0,2

Links

Table of n, a(n) for n=0..24.

Example

(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, ...

Mathematica

nmax = 24; CoefficientList[Series[(1 + x)^(3/4), {x, 0, nmax}], x] // Numerator
Table[Binomial[3/4, n], {n, 0, 24}] // Numerator

Prog

(PARI) my(x='x+O('x^30)); apply(numerator, Vec((1 + x)^(3/4))) \\ Michel Marcus, Aug 02 2023

Crossrefs

Denominators are A088802, A123854.

Cf. A002596, A067002, A364658, A364660.

Sequence in context: A093310 A256402 A170919 * A280779 A241591 A248592

Adjacent sequences: A364658 A364659 A364660 * A364662 A364663 A364664

Keyword

sign,frac

Author

Ilya Gutkovskiy, Aug 01 2023

Status

approved