login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082138 A transform of C(n,3). 10
1, 4, 20, 80, 280, 896, 2688, 7680, 21120, 56320, 146432, 372736, 931840, 2293760, 5570560, 13369344, 31752192, 74711040, 174325760, 403701760, 928514048, 2122317824, 4823449600, 10905190400, 24536678400, 54962159616, 122607894528 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fourth row of number array A082137. C(n,3) has e.g.f. (x^3/3!)exp(x). The transform averages the binomial and inverse binomial transforms.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

FORMULA

a(n) = (2^(n-1)+0^n/2)C(n+3, n) = sum{j=0..n, C(n+3, j+3)C(j+3, 3)(1+(-1)^j)/2 }.

G.f.: (1-4x+12x^2-16x^3+8x^4)/(1-2x)^4.

E.g.f.: (x^3/3!)exp(x)cosh(x) (preceded by 3 zeros).

a(n) = ceil(binomial(n+3,3)*2^(n-1)). - Zerinvary Lajos, Nov 01 2006

EXAMPLE

a(0)=(2^(-1)+0^0/2)C(3,0)=2*(1/2)=1 (use 0^0=1).

MAPLE

[seq (ceil(binomial(n+3, 3)*2^(n-1)), n=0..26)]; # Zerinvary Lajos, Nov 01 2006

PROG

(MAGMA) [(Ceiling(Binomial(n+3, 3)*2^(n-1))) : n in [0..30]]; // Vincenzo Librandi, Sep 22 2011

CROSSREFS

Cf. A080929, A082139, A082140, A082141, A080951, A057711.

Sequence in context: A295116 A303508 A258627 * A074358 A255050 A292540

Adjacent sequences:  A082135 A082136 A082137 * A082139 A082140 A082141

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 06 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 04:50 EDT 2019. Contains 323539 sequences. (Running on oeis4.)