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 A228837 a(n) = Sum_{k=0..[n/2]} binomial((n-k)^2, (n-2*k)*k). 3
 1, 1, 2, 5, 38, 597, 14472, 554653, 44421258, 8933194659, 3408672951784, 1984802013951149, 1803179670478111304, 3323206887194925488269, 15156709454119350064982141, 132889643918499982093215167857, 1784438297905511051093397284187186 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals the antidiagonal sums of triangle A228836. LINKS G. C. Greubel, Table of n, a(n) for n = 0..86 FORMULA Limit n->infinity a(n)^(1/n^2) = ((1-r)^2/(r*(1-2*r)))^((1-3*r)*(1-r)/(3*(1-2*r))) = 1.36198508972775011599..., where r = 0.195220321930105755... is the root of the equation (1-3*r+3*r^2)^(3*(2*r-1)) = (r*(1-2*r))^(4*r-1) * (1-r)^(4*(r-1)). - Vaclav Kotesovec, added Sep 05 2013, simplified Mar 04 2014 MATHEMATICA Table[Sum[Binomial[(n-k)^2, (n-2*k)*k], {k, 0, Floor[n/2]}], {n, 0, 15}] (* Vaclav Kotesovec, Sep 05 2013 *) PROG (PARI) {a(n)=sum(k=0, n\2, binomial((n-k)^2, (n-2*k)*k))} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A228836, A207138. Cf. variants: A209331, A228833, A123165. Sequence in context: A221681 A347070 A290711 * A206155 A135378 A077398 Adjacent sequences: A228834 A228835 A228836 * A228838 A228839 A228840 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 05 2013 STATUS approved

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Last modified December 9 09:46 EST 2022. Contains 358700 sequences. (Running on oeis4.)