A364660 -id:A364660 - cp's OEIS frontend

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

Ilya Gutkovskiy, Aug 01 2023

			(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, ...

Denominators are A088802, A123854.

Cf. A002596, A067002, A364658, A364660.

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

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

A364713 a(n) is the numerator of coefficient of x^n in expansion of (1 + x)^(1/n).

Original entry on oeis.org

1, -1, 5, -77, 399, -124729, 81549, -23960365, 283583443, -478398640447, 19740912828, -11911591259019739, 18262332208600, -4514446693068714225, 142267808222130386191, -1912831808055538077885, 39773048560156838355, -43025628065750129034887540875, 86435429204640847578555

Offset: 1

Ilya Gutkovskiy, Aug 04 2023

			1, -1/8, 5/81, -77/2048, 399/15625, -124729/6718464, 81549/5764801, ...

Denominators are A145921.

Cf. A002596, A067622, A344745, A364660.

Table[SeriesCoefficient[(1 + x)^(1/n), {x, 0, n}], {n, 1, 21}] // Numerator
Table[Binomial[1/n, n], {n, 1, 21}] // Numerator

a(n) = numerator(binomial(1/n, n)); \\ Michel Marcus, Aug 05 2023

cp's OEIS Frontend

A364661 Numerators of coefficients in expansion of (1 + x)^(3/4).

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