A154603 Binomial transform of reduced tangent numbers (A002105).

1, 1, 2, 4, 11, 31, 110, 400, 1757, 7861, 41402, 220540, 1358183, 8405203, 59340710, 418689544, 3335855897, 26440317193, 234747589106, 2065458479476, 20224631361251, 195625329965671, 2094552876276830, 22092621409440256

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