A073398 Ninth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.

1, 20, 240, 2200, 16940, 115104, 711040, 4072640, 21930480, 112157760, 549010176, 2587777920, 11802273600, 52287866880, 225756241920, 952486588416, 3935984616960, 15961485957120, 63628396339200, 249702113464320, 965924035135488, 3687247950397440

Offset: 0

Author

Wolfdieter Lang, Aug 02 2002

Keywords

• nonn
• easy

Comments

For a(n) in terms of U(n+1) and U(n), with U(n) = A002605(n), see A073387 and the row polynomials of triangles A073405 and A073406.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-160,600,-660,-2496,7680,1920,-28320,7040, 66560,-14080,-113280,-15360,122880,79872,-42240,-76800,-40960,-10240,-1024).

Crossrefs

Tenth (m=9) column of triangle A073387.

Cf. A002605, A073397, A073405, A073406.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^10 )); // G. C. Greubel, Oct 06 2022

Mathematica

CoefficientList[Series[1/(1-2*x-2*x^2)^10, {x,0,30}], x] (* G. C. Greubel, Oct 06 2022 *)

SageMath

def A073398_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-2*x-2*x^2)^10 ).list()
A073398_list(30) # G. C. Greubel, Oct 06 2022

Formula

a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A002605(k) and c(k) = A073397(k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9)*binomial(n-k, k)*2^(n-k).

G.f.: 1/(1-2*x*(1+x))^10.