A364703 Numerators of coefficients in expansion of sqrt( 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + ... ).

1, 1, 7, 17, 139, 263, 995, 1969, 32371, 66635, 268121, 527959, 4146719, 8259235, 33398491, 67666673, 2171753923, 4309377779, 17069564957, 34059684283, 274173644357, 552586858969, 2214430477093, 4407001803383, 70069816438007, 139923827220319, 562011390816205, 1129932221061107

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Example

The coefficients are 1, 1/2, 7/8, 17/16, 139/128, 263/256, 995/1024, 1969/2048, 32371/32768, 66635/65536, ...

Mathematica

nmax = 27; CoefficientList[Series[Sqrt[1 + x/(1 - x)^2], {x, 0, nmax}], x] // Numerator

Prog

(PARI) my(x='x+O('x^30)); apply(numerator, Vec(sqrt(1 + x/(1 - x)^2))) \\ Michel Marcus, Aug 04 2023

Crossrefs

The denominators appear to be A046161.

Cf. A001790, A261419, A261420.

Sequence in context: A118108 A227506 A244279 * A325584 A214149 A147643

Adjacent sequences: A364700 A364701 A364702 * A364704 A364705 A364706

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Aug 03 2023

Status

approved