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 A228833 a(n) = Sum_{k=0..[n/2]} binomial((n-k)*k, k^2). 3
 1, 1, 2, 3, 5, 20, 77, 437, 5509, 54475, 1031232, 31874836, 789351469, 47552777430, 3302430043985, 223753995897916, 39177880844093733, 5954060239110086680, 1226026438114057710320, 551315671593483499670137, 188615011023291125237647365, 124995445742889226418307452940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals antidiagonal sums of triangle A228832. LINKS Table of n, a(n) for n=0..21. FORMULA Limit n->infinity a(n)^(1/n^2) = ((1-r)/(1-2*r))^(r/2) = 1.171233876693210503..., where r = A323773 = 0.366320150305283... is the root of the equation (1-2*r)^(4*r-1) * (1-r)^(1-2*r) = r^(2*r). - Vaclav Kotesovec, Sep 06 2013 MATHEMATICA Table[Sum[Binomial[(n-k)*k, k^2], {k, 0, Floor[n/2]}], {n, 0, 15}] (* Vaclav Kotesovec, Sep 06 2013 *) PROG (PARI) {a(n)=sum(k=0, n\2, binomial(n*k-k^2, k^2))} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A228832. Sequence in context: A054798 A127078 A184252 * A320950 A291673 A076383 Adjacent sequences: A228830 A228831 A228832 * A228834 A228835 A228836 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 04 2013 STATUS approved

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Last modified June 8 00:26 EDT 2023. Contains 363157 sequences. (Running on oeis4.)