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

0,2

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).

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.

Mathematica

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

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^10 )); // G. C. Greubel, Oct 06 2022
(SageMath)
def A073398_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-2*x-2*x^2)^10 ).list()
A073398_list(30) # G. C. Greubel, Oct 06 2022

Crossrefs

Tenth (m=9) column of triangle A073387.

Cf. A002605, A073397, A073405, A073406.

Sequence in context: A278320 A061139 A061121 * A040075 A138442 A341196

Adjacent sequences: A073395 A073396 A073397 * A073399 A073400 A073401

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved