A364700 Numerators of coefficients in expansion of sqrt( Sum_{j>=1} x^prime(j) ).

1, 1, -1, 9, -37, 183, -565, 1081, -25453, 96427, -404927, 1279359, -12561457, 33077619, -194103389, 577222425, -25302548477, 74326953907, -423955653883, 1225808143651, -14456976876619, 42661352483945, -250437691682371, 741244373831663, -17624677238323753, 52507307961906687, -314022434935401067

Offset

1,4

Links

Table of n, a(n) for n=1..27.

Example

The coefficients are 1, 1/2, -1/8, 9/16, -37/128, 183/256, -565/1024, 1081/2048, -25453/32768, ...

Mathematica

nmax = 27; CoefficientList[Series[Sqrt[Sum[x^Prime[j], {j, 1, nmax}]], {x, 0, nmax}], x] // Numerator // Rest

Crossrefs

The denominators appear to be A046161.

Cf. A000040, A001790, A010051, A073749.

Sequence in context: A232250 A201441 A183327 * A199894 A232258 A370244

Adjacent sequences: A364697 A364698 A364699 * A364701 A364702 A364703

Keyword

sign,frac

Author

Ilya Gutkovskiy, Aug 03 2023

Status

approved