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A154603 Binomial transform of reduced tangent numbers (A002105). 2
1, 1, 2, 4, 11, 31, 110, 400, 1757, 7861, 41402, 220540, 1358183, 8405203, 59340710, 418689544, 3335855897, 26440317193, 234747589106, 2065458479476, 20224631361251, 195625329965671, 2094552876276830, 22092621409440256 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A154604.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

FORMULA

G.f: 1/(1-x-x^2/(1-x-3x^2/(1-x-6x^2/(1-x-10x^2/(1-x-15x^2..... (continued fraction);

E.g.f.: exp(x)*(sec(x/sqrt(2))^2);

G.f.: 1/(x*Q(0)), where Q(k)= 1/x - 1 - (k+1)*(k+2)/2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 26 2013

G.f.: 1/Q(0), where Q(k)= 1 - x - 1/2*x^2*(k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 04 2013

a(n) ~ n! * 2^(2+n/2)*n*(exp(sqrt(2)*Pi)+(-1)^n) / (Pi^(n+2)*exp(Pi/sqrt(2))). - Vaclav Kotesovec, Oct 02 2013

G.f.: T(0)/(1-x), where T(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - 2*(1-x)^2/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 14 2013

MATHEMATICA

With[{nn=30}, CoefficientList[Series[Exp[x]Sec[x/Sqrt[2]]^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 30 2013 *)

CROSSREFS

Sequence in context: A115625 A056323 A081557 * A063254 A280766 A123443

Adjacent sequences:  A154600 A154601 A154602 * A154604 A154605 A154606

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 12 2009

EXTENSIONS

Typo in e.g.f. fixed by Vaclav Kotesovec, Oct 02 2013

STATUS

approved

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Last modified October 17 14:39 EDT 2019. Contains 328114 sequences. (Running on oeis4.)