A103424 Expansion of e.g.f.: 1 + sinh(2*x).

1, 2, 0, 8, 0, 32, 0, 128, 0, 512, 0, 2048, 0, 8192, 0, 32768, 0, 131072, 0, 524288, 0, 2097152, 0, 8388608, 0, 33554432, 0, 134217728, 0, 536870912, 0, 2147483648, 0, 8589934592, 0, 34359738368, 0, 137438953472, 0, 549755813888, 0, 2199023255552

Offset: 0

Author

Paul Barry, Feb 05 2005

Keywords

• easy
• nonn

Comments

Binomial transform is A103425.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,4).

Crossrefs

Cf. A077957, A103425, A199572.

Programs

Mathematica

With[{nn=50},CoefficientList[Series[1+Sinh[2x],{x,0,nn}],x] Range[ 0,nn-1]!] (* Harvey P. Dale, Jun 29 2014 *)
CoefficientList[Series[(1 + 2 x - 4 x^2)/(1 - 4 x^2), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 30 2014 *)

Formula

G.f.: (1+2*x-4*x^2)/(1-4*x^2).

E.g.f.: 1 + sinh(2*x).

a(n) = 0^n+(2^n-(-2)^n)/2.

a(n) = Sum_{k=0..n} binomial(n, k)*(-1)^(k(n-k)).

a(n+1) = 2*A199572(n) = 2*A077957(n)^2. [Ralf Stephan, Jul 17 2013]