The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A012748

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A012748

Expansion of e.g.f. sec(arctanh(x)*cos(x)), only even powers.
(history; published version)

#15 by OEIS Server at Fri Jun 21 14:35:07 EDT 2024

LINKS

Stefano Spezia, <a href="/A012748/b012748_1.txt">Table of n, a(n) for n = 0..150</a>

#14 by Alois P. Heinz at Fri Jun 21 14:35:07 EDT 2024

STATUS

proposed

approved

Discussion

Fri Jun 21

14:35

OEIS Server: Installed first b-file as b012748.txt.

#13 by Stefano Spezia at Fri Jun 21 13:24:29 EDT 2024

STATUS

editing

proposed

#12 by Stefano Spezia at Fri Jun 21 13:24:11 EDT 2024

EXTENSIONS

a(14)-a(16) from Stefano Spezia, Jun 21 2024

STATUS

proposed

editing

Discussion

Fri Jun 21

13:24

Stefano Spezia: Put back. Thanks

#11 by Stefano Spezia at Fri Jun 21 12:50:24 EDT 2024

STATUS

editing

proposed

Discussion

Fri Jun 21

13:13

Michel Marcus: yes for extension : a(14)-a(16) from Stefano Spezia, Jun 21 2024

#10 by Stefano Spezia at Fri Jun 21 09:48:29 EDT 2024

LINKS

Stefano Spezia, <a href="/A012748/b012748_1.txt">Table of n, a(n) for n = 0..150</a>

EXTENSIONS

a(14)-a(16) from Stefano Spezia, Jun 21 2024

#9 by Stefano Spezia at Fri Jun 21 09:39:06 EDT 2024

NAME

Expansion of e.g.f. sec(arctanh(x)*cos(x)), only even powers.

#8 by Stefano Spezia at Fri Jun 21 09:31:58 EDT 2024

EXAMPLE

E.g.f. = 1 + 1/2!*x^2 + 1/42!* + x^4 /4! + 25/6!*x^6 /6! + 3617/8!*x^8 /8! + ...

#7 by Stefano Spezia at Fri Jun 21 09:30:11 EDT 2024

NAME

sec(arctanh(x)*cos(x))=1+1/2!*x^2+1/4!*x^4+25/6!*x^6+3617/8!*x^8...

Expansion of e.g.f. sec(arctanh(x)*cos(x)).

EXAMPLE

E.g.f. = 1 + 1/2!*x^2 + 1/4!*x^4 + 25/6!*x^6 + 3617/8!*x^8 + ...

#6 by Stefano Spezia at Fri Jun 21 09:27:55 EDT 2024

MATHEMATICA

nmax=32; DeleteCases[CoefficientList[Series[Sec[ArcTanh[x]Cos[x]], {x, 0, nmax}], x], 0](2Range[0, nmax/2])! (* Stefano Spezia, Jun 21 2024 *)

EXTENSIONS

a(14)-a(16) from Stefano Spezia, Jun 21 2024