A364660 Numerators of coefficients in expansion of (1 + x)^(1/4).

1, 1, -3, 7, -77, 231, -1463, 4807, -129789, 447051, -3129357, 11094993, -159028233, 574948227, -4188908511, 15359331207, -906200541213, 3358272593907, -25000473754641, 93422822977869, -1401342344668035, 5271716439465465, -39777496770512145, 150462705175415505, -4564035390320936985

Offset

0,3

Links

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

Example

(1 + x)^(1/4) = 1 + x/4 - 3*x^2/32 + 7*x^3/128 - 77*x^4/2048 + 231*x^5/8192 - 1463*x^6/65536 + ...
Coefficients are 1, 1/4, -3/32, 7/128, -77/2048, 231/8192, -1463/65536, ...

Mathematica

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

Prog

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

Crossrefs

Denominators are A088802, A123854.

Cf. A002596, A004130, A008545, A067622, A364661.

Sequence in context: A103737 A354480 A108537 * A219292 A181554 A116294

Adjacent sequences: A364657 A364658 A364659 * A364661 A364662 A364663

Keyword

sign,frac

Author

Ilya Gutkovskiy, Aug 01 2023

Status

approved