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

0,2

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).

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]

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 *)

Crossrefs

Cf. A077957, A103425, A199572.

Sequence in context: A167029 A094030 A199573 * A347596 A211163 A239275

Adjacent sequences: A103421 A103422 A103423 * A103425 A103426 A103427

Keyword

easy,nonn

Author

Paul Barry, Feb 05 2005

Status

approved