A034009 Convolution of A000295(n+2) (n>=0) with itself.

1, 8, 38, 140, 443, 1268, 3384, 8584, 20965, 49744, 115402, 262996, 590831, 1311900, 2884956, 6293040, 13633305, 29362200, 62916910, 134220380, 285215651, 603983108, 1275072128, 2684358680, 5637149133, 11811165088

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-26,44,-41,20,-4).

Formula

(2^(n+2)-n-3) '*' (2^(n+2)-n-3) where '*' denotes the convolution product.

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

Partial sums of A045889.

a(n) = (n-3)*2^(n+4)+binomial(n+3,3)+4*(binomial(n+1,2)+4*n+12)

= 2^(n+4)*(n-3)+(n+7)*(n*(n+11)+42)/6.

a(n) = binomial(n+3,3)*hypergeom([2,-n],[-n-3],2). - Peter Luschny, Sep 19 2014

a(n) = Sum_{k=0..n+4} Sum_{i=0..n+4} (i-k) * C(n-k+4,i+2). - Wesley Ivan Hurt, Sep 19 2017

Maple

seq(16*(n-3)*2^n+(n+7)*(n^2+11*n+42)/6, n=0..100); # Robert Israel, Sep 19 2014

Mathematica

Table[Sum[ k Binomial[n + 5, k + 4], {k, 0, n+1}], {n, 0, 26}] (* Zerinvary Lajos, Jul 08 2009 *)
Table[(16 (n-3) 2^n + (n + 7) (n^2 + 11 n + 42) / 6), {n, 0, 40}] (* Vincenzo Librandi, Sep 20 2014 *)

Prog

(Magma) [(16*(n-3)*2^n+(n+7)*(n^2+11*n+42) div 6): n in [0..30]]; // Vincenzo Librandi, Sep 20 2014

Crossrefs

Cf. A000295, A045889.

Sequence in context: A359931 A211063 A065762 * A038732 A038799 A156934

Adjacent sequences: A034006 A034007 A034008 * A034010 A034011 A034012

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

Edited by Peter Luschny, Sep 20 2014

Status

approved