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A073379 Ninth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself. 2
1, 10, 75, 440, 2255, 10362, 43945, 174460, 656370, 2359500, 8158722, 27275040, 88524930, 279892380, 864508590, 2614740216, 7759693095, 22634343270, 64990287285, 183929970840, 513661549401, 1416970676550 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
For a(n) in terms of U(n+1) and U(n), with U(n) = A001045(n+1), see A073370 and the row polynomials of triangles A073399 and A073400.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-25,-60,330,12,-1770,960,5835,-4070,-13597, 8140,23340,-7680,-28320,-384,21120,7680,-6400,-5120,-1024).
FORMULA
a(n) = Sum_{k=0..n} (b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073378(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9) * binomial(n-k, k) * 2^k.
G.f.: 1/(1-(1+2*x)*x)^10 = 1/((1+x)*(1-2*x))^10.
MATHEMATICA
CoefficientList[Series[1/((1+x)*(1-2*x))^10, {x, 0, 40}], x] (* G. C. Greubel, Oct 01 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^10 )); // G. C. Greubel, Oct 01 2022
(SageMath)
def A073379_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1+x)*(1-2*x))^10 ).list()
A073379_list(40) # G. C. Greubel, Oct 01 2022
CROSSREFS
Tenth (m=9) column of triangle A073370.
Sequence in context: A026969 A026979 A274251 * A283238 A316462 A022734
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved

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Last modified July 15 10:33 EDT 2024. Contains 374332 sequences. (Running on oeis4.)