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A073392 Fifth convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 2
1, 12, 96, 616, 3444, 17472, 82432, 367488, 1565280, 6421376, 25525248, 98773248, 373450112, 1383674880, 5036089344, 18041821184, 63727070976, 222249968640, 766234140672, 2614196680704, 8834194123776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..n} b(k)*c(n-k) with b(k) := A002605(k) and c(k) := A073391(k).

a(n) = (2^n)*Sum_{k=0..floor(n/2)} binomial(n-k+5, 5)*binomial(n-k, k)*(1/2)^k.

a(n) = (n+4)*(n+8)*((19*n^2+158*n+275)*(n+1)*U(n+1)+2*(7*n^2+52*n+65)*(n+2)*U(n))/(2^6*3^4*5), with U(n) := A002605(n), n>=0.

G.f.: 1/(1-2*x*(1+x))^6.

EXAMPLE

x^6 + 12*x^7 + 96*x^8 + 616*x^9 + 3444*x^10 + ... + 222249968640*x^23 + 766234140672*x^24 + 2614196680704*x^25 + 8834194123776*x^26 + ... - Zerinvary Lajos, Jun 03 2009

MATHEMATICA

CoefficientList[Series[1/(1-2*x*(1+x))^6, {x, 0, 20}], x] (* Harvey P. Dale, May 12 2018 *)

PROG

(Sage) taylor( mul(x/(1 - 2*x - 2*x^2) for i in range(1, 7)), x, 0, 26) # Zerinvary Lajos, Jun 03 2009

(GAP) List([0..25], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+5, 5)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018

CROSSREFS

Sixth (m=5) column of triangle A073387.

Cf. A002605, A073391.

Sequence in context: A121627 A138162 A264418 * A038845 A204623 A270568

Adjacent sequences:  A073389 A073390 A073391 * A073393 A073394 A073395

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified June 22 12:22 EDT 2021. Contains 345375 sequences. (Running on oeis4.)