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A123165 Row sums of A123163. 6

%I

%S 1,1,2,5,11,143,1847,24127,2101931,96398196,9362963203,3376252046640,

%T 551993132054154,434634824535802596,528116646162507517308,

%U 372831439174848001477184,2029862948426766042724907818

%N Row sums of A123163.

%H Seiichi Manyama, <a href="/A123165/b123165.txt">Table of n, a(n) for n = 0..94</a>

%F Limit n->infinity a(n)^(1/n^2) = (1-2*r)^r / r^(2*r) = 1.2915356633069917227119166..., where r = A323778 = 0.365498498219858044579736... is the root of the equation (1-r)^(2-2*r) * r^(2*r) = 1-2*r. - _Vaclav Kotesovec_, Mar 04 2014

%t t[n_, m_] = (n^2 - 2*n*m + m^2)!/((m^2)!(n^2 - 2*n*m)!); a = Table[Sum[t[n, m], {m, 0, n}], {n, 0, 20}]

%t Table[Sum[Binomial[(n-k)^2,k^2], {k, 0, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Mar 04 2014 *)

%o (PARI) {a(n) = sum(k=0, n\2, binomial((n-k)^2, k^2))} \\ _Seiichi Manyama_, Jan 28 2019

%Y Cf. A123163, A206851.

%K nonn

%O 0,3

%A _Roger L. Bagula_, Oct 02 2006

%E Edited by _N. J. A. Sloane_, Oct 04 2006

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Last modified July 10 14:17 EDT 2020. Contains 335576 sequences. (Running on oeis4.)