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A073393 Sixth convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 1
1, 14, 126, 896, 5488, 30240, 153888, 735744, 3344544, 14581952, 61378240, 250693632, 997593856, 3880249856, 14791776768, 55385874432, 204082373376, 741186464256, 2656771815936, 9410113241088 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (14, -70, 112, 196, -728, -168, 1920, 336, -2912, -1568, 1792, 2240, 896, 128).

FORMULA

a(n) = Sum_{k=0..n} b(k)*c(n-k) with b(k) := A002605(k) and c(k) := A073392(k).

a(n) = (2^n)*Sum_{k=0..floor(n/2)} binomial(n-k+6, 6)*binomial(n-k, k)*(1/2)^k.

a(n) = ((54340 + 59802*n + 24583*n^2 + 4747*n^3 + 433*n^4 + 15*n^5)*(n+1)*U(n+1) + (23420 + 32768*n + 15333*n^2 + 3201*n^3 + 307*n^4 + 11*n^5)*(n+2)*U(n))/(2^7*3^5*5), with U(n) := A002605(n), n >= 0.

G.f.: 1/(1-2*x*(1+x))^7.

a(0)=1, a(1)=14, a(2)=126, a(3)=896, a(4)=5488, a(5)=30240, a(6)=153888, a(7)=735744, a(8)=3344544, a(9)=14581952, a(10)=61378240, a(11)=250693632, a(12)=997593856, a(13)=3880249856, a(n) = 14*a(n-1) - 70*a(n-2) + 112*a(n-3) + 196*a(n-4) - 728*a(n-5) - 168*a(n-6) + 1920*a(n-7) + 336*a(n-8) - 2912*a(n-9) - 1568*a(n-10) + 1792*a(n-11) + 2240*a(n-12) + 896*a(n-13) + 128*a(n-14). - Harvey P. Dale, Jan 24 2013

EXAMPLE

x^7 + 14*x^8 + 126*x^9 + 896*x^10 + 5488*x^11 + ... + 204082373376*x^23 + 741186464256*x^24 + 2656771815936*x^25 + 9410113241088*x^26 + ... - Zerinvary Lajos, Jun 03 2009

MATHEMATICA

CoefficientList[Series[1/(1-2x(1+x))^7, {x, 0, 30}], x] (* or *) LinearRecurrence[ {14, -70, 112, 196, -728, -168, 1920, 336, -2912, -1568, 1792, 2240, 896, 128}, {1, 14, 126, 896, 5488, 30240, 153888, 735744, 3344544, 14581952, 61378240, 250693632, 997593856, 3880249856}, 30](* Harvey P. Dale, Jan 24 2013 *)

PROG

(Sage) taylor( mul(x/(1 - 2*x - 2*x^2) for i in range(1, 8)), x, 0, 26) # Zerinvary Lajos, Jun 03 2009

CROSSREFS

Seventh (m=6) column of triangle A073387.

Sequence in context: A026870 A090296 A088625 * A020918 A275559 A222477

Adjacent sequences:  A073390 A073391 A073392 * A073394 A073395 A073396

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified May 10 19:32 EDT 2021. Contains 343780 sequences. (Running on oeis4.)