cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A143991 Numerators of numbers with g.f. exp(1-(1-x)^(1/2)).

Original entry on oeis.org

1, 1, 1, 7, 37, 133, 2431, 27007, 176761, 5329837, 12994393, 866792053, 5213746711, 841146804577, 10532583170701, 569600638022431, 16539483668991901, 3333075288160853, 16955228098102446847, 932411737877492011, 10996483739066355827053, 66024590609554132070857
Offset: 0

Views

Author

N. J. A. Sloane, Dec 02 2008

Keywords

Examples

			1, 1/2, 1/4, 7/48, 37/384, 133/1920, 2431/46080, 27007/645120, 176761/5160960, ...

Links

Crossrefs

Cf. A143968 (denominators), A001515.
Cf. A381845.

Programs

  • Maple
    S:= series(exp(1-(1-x)^(1/2)),x,21):
seq(numer(coeff(S,x,i)),i=0..20); # Robert Israel, Mar 23 2023
  • Mathematica
    CoefficientList[Series[Exp[1-Sqrt[1-x]],{x,0,30}],x]//Numerator (* Harvey P. Dale, Nov 23 2024 *)

Formula

Conjecture: a(n) = numerator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ) for n > 0. See A381845 for the numerators of this integral. - Stefano Spezia, Mar 12 2025

A144525 Numerators of expansion of exp(1-sqrt(1-3*x)).

Original entry on oeis.org

1, 3, 9, 63, 999, 10773, 196911, 6562701, 128858769, 1295150391, 9472912497, 1895674219911, 11402464056957, 5518764184829697, 207312834548907783, 11211449358195509373, 976639971170302762149, 590444288071830626391, 1001189263964851383868503
Offset: 0

Views

Author

N. J. A. Sloane, Dec 20 2008

Keywords

Examples

			1 + (3/2)*x + (9/4)*x^2 + (63/16)*x^3 + (999/128)*x^4 + (10773/640)*x^5 + (196911/5120)*x^6 + ...

Crossrefs

Cf. A144526, A001511, A143991/A143968.

Programs

  • Mathematica
    CoefficientList[Series[Exp[1-Sqrt[1-3x]],{x,0,20}],x]//Numerator (* Harvey P. Dale, Dec 27 2022 *)

A144526 Denominators of expansion of exp(1-sqrt(1-3*x)).

Original entry on oeis.org

1, 2, 4, 16, 128, 640, 5120, 71680, 573440, 2293760, 6553600, 504627200, 1153433600, 209924915200, 2938948812800, 58778976256000, 1880927240192000, 415269650432000, 255806104666112000, 15260018802688000, 194412639546245120000, 418734915945758720000
Offset: 0

Views

Author

N. J. A. Sloane, Dec 20 2008

Keywords

Examples

			1 + (3/2)*x + (9/4)*x^2 + (63/16)*x^3 + (999/128)*x^4 + (10773/640)*x^5 + (196911/5120)*x^6 + ...

Crossrefs

Cf. A144525, A001511, A143991/A143968.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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