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 A112556 Sums of squared terms in rows of triangle A112555. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 28 15:08 EDT 2023. Contains 361595 sequences. (Running on oeis4.)