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A073394 Seventh convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 1
1, 16, 160, 1248, 8304, 49344, 269184, 1372800, 6628512, 30584576, 135804416, 583471616, 2436145920, 9919484928, 39503038464, 154230921216, 591550292736, 2232748892160, 8305370185728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = Sum_{k=0..n} b(k)*c(n-k) with b(k) := A002605(k) and c(k) := A073393(k).

a(n) = (2^n)*Sum_{k=0..floor(n/2)} binomial(n-k+7, 7)*binomial(n-k, k)*(1/2)^k.

a(n) = ((2322320+2869040*n + 1379232*n^2 + 332247*n^3 + 42533*n^4 + 2757*n^5 + 71*n^6)*(n+1)*U(n+1) + 4*(235900 + 375554*n + 207009*n^2 + 54174*n^3 + 7318*n^4 + 492*n^5 + 13*n^6)*(n+2)*U(n))/(2^8*3^6*5*7), with U(n) := A002605(n), n >= 0.

G.f.: 1/(1-2*x*(1+x))^8.

EXAMPLE

x^8 + 16*x^9 + 160*x^10 + 1248*x^11 + ... + 154230921216*x^23 + 591550292736*x^24 + 2232748892160*x^25 + 8305370185728*x^26 + ... - Zerinvary Lajos, Jun 03 2009

PROG

(Sage) taylor( mul(x/(1 - 2*x - 2*x^2) for i in range(1, 9)), x, 0, 26) # Zerinvary Lajos, Jun 03 2009

CROSSREFS

Eighth (m=7) column of triangle A073387.

Sequence in context: A144453 A121036 A224058 * A038846 A079767 A079768

Adjacent sequences:  A073391 A073392 A073393 * A073395 A073396 A073397

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified June 24 10:11 EDT 2021. Contains 345416 sequences. (Running on oeis4.)