A112556 - OEIS

A112556

Sums of squared terms in rows of triangle A112555.

1, 2, 2, 4, 10, 32, 112, 408, 1514, 5680, 21472, 81644, 311896, 1196132, 4602236, 17757184, 68680170, 266200112, 1033703056, 4020716124, 15662273840, 61092127492, 238582873476, 932758045124, 3650336341240, 14298633670932, 56055986383412, 219931273282348, 863504076182884, 3392593262288780, 13337336618626132

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OFFSET

0,2

COMMENTS

First differences form A072547 and equals the unsigned central terms of triangle A112555.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: ( 2*(1+x)/(1-x) + x/(1-4*x)^(1/2) )/(2+x).

a(n) ~ 2^(2*n) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Mar 26 2016

a(n) = (1/3)*(4 - (-1/2)^n) - Sum_{j=0..n-1} binomial(2*j, j)*(-1/2)^(n-j). - G. C. Greubel, Jan 13 2022

MATHEMATICA

CoefficientList[Series[(2(1+x)/(1-x)+x/(1-4x)^(1/2))/(2+x), {x, 0, 30}], x] (* Harvey P. Dale, May 26 2011 *)

PROG

(PARI) {a(n)=local(x=X+X*O(X^n)); polcoeff((2*(1+x)/(1-x)+x/(1-4*x)^(1/2))/(2+x), n, X)}

(Magma) [(1/3)*(4 - (-1/2)^n) + (n+1)*Catalan(n) - (&+[(j+1)*Catalan(j)*(-1/2)^(n-j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Jan 13 2022

(Sage) [(1/3)*(4 - (-1/2)^n) - sum( binomial(2*j, j)*(-1/2)^(n-j) for j in (0..n-1)) for n in (0..30)] # G. C. Greubel, Jan 13 2022

CROSSREFS

Cf. A072547, A112555.

Sequence in context: A309159 A002420 A284016 * A254400 A054100 A034165

Adjacent sequences: A112553 A112554 A112555 * A112557 A112558 A112559

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 21 2005

STATUS

approved