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.

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A012007 cosh(log(cos(x))) = 1+3/4!*x^4+30/6!*x^6+693/8!*x^8+25260/10!*x^10...

Original entry on oeis.org

1, 0, 3, 30, 693, 25260, 1351383, 99680490, 9695756073, 1202439837720, 185185594118763, 34674437196568950, 7757267081778543453, 2043536254646561946180, 626129820701814932734143, 220771946624511552276841410, 88759695789769644718332394833
Offset: 0

Views

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

Crossrefs

Cf. A012003, A012008, A012009.

Programs

  • Mathematica
    terms = 15; s = Cosh[Log[Cos[x]]] + O[x]^(2*terms); CoefficientList[s, x^2] * Table[(2n)!, {n, 0, terms-1}] (* Jean-François Alcover, May 22 2017 *)

Formula

a(n) = (1/2)*((-1)^n+A000364(n)). Also cosh(log(cos(x))) = 1/2*(cos(x)+1/cos(x)) is the reciprocal of the e.g.f. of A012009. - Peter Bala, Dec 02 2011

Extensions

Confirmed by N. J. A. Sloane, Dec 17 2011

A012009 Expansion of e.g.f. sech(log(cos(x))) (even exponents only).

Original entry on oeis.org

1, 0, -3, -30, -63, 12540, 602877, 6625710, -1991169183, -241970036520, -7540177734243, 2917041754949850, 699983161534169697, 46722975483964508820, -21334067257986056115363, -8882421213380429461235610, -1081286159351846822872767423
Offset: 0

Views

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

Examples

			1 - (3/4!)*x^4 - (30/6!)*x^6 - (63/8!)*x^8 + (12540/10!)*x^10 ...

Crossrefs

Cf. A012003, A012007, A012008.

Programs

  • Mathematica
    With[{nn=40},Take[CoefficientList[Series[Sech[Log[Cos[x]]],{x,0,nn}], x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Dec 16 2011 *)

Formula

E.g.f.: sech(log(cos(x))) = 2*cos(x)/(1+cos^2(x)) is the reciprocal of the e.g.f. of A012007. - Peter Bala, Dec 02 2011

Extensions

More terms from Harvey P. Dale, Dec 16 2011
New name from Michel Marcus, Aug 04 2024
Showing 1-2 of 2 results.

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

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