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A123165 Row sums of A123163. 6
1, 1, 2, 5, 11, 143, 1847, 24127, 2101931, 96398196, 9362963203, 3376252046640, 551993132054154, 434634824535802596, 528116646162507517308, 372831439174848001477184, 2029862948426766042724907818 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..94

FORMULA

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

MATHEMATICA

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}]

Table[Sum[Binomial[(n-k)^2, k^2], {k, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 04 2014 *)

PROG

(PARI) {a(n) = sum(k=0, n\2, binomial((n-k)^2, k^2))} \\ Seiichi Manyama, Jan 28 2019

CROSSREFS

Cf. A123163, A206851.

Sequence in context: A283300 A069506 A239900 * A098438 A225955 A236073

Adjacent sequences:  A123162 A123163 A123164 * A123166 A123167 A123168

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Oct 02 2006

EXTENSIONS

Edited by N. J. A. Sloane, Oct 04 2006

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)