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A123114 a(n) = Sum_{r>0,s>0} binomial(r*s-1,n-1)/2^(r+s). 1
1, 3, 13, 83, 701, 7363, 92541, 1354627, 22636861, 425241347, 8871085565, 203487078403, 5090418231549, 137920771272963, 4023549748488445, 125743894742698243, 4191213031967650813, 148414827031140706307 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..400

M. Maia and M. Mendez, On the arithmetic product of combinatorial species

FORMULA

a(n) = 1/(n-1)!*Sum_{k=1..n} Stirling1(n,k)*b(k)^2, where b(n) = Sum_{k=1..n} (k-1)!*Stirling2(n,k).

a(n) ~ c * (n-1)! / (log(2))^(2*n), where c = 2^(-log(2)/2) = 0.7864497045594053649114085152934509198700275589579678941719548714254307448... - Vaclav Kotesovec, Jun 07 2019

MATHEMATICA

Table[Sum[StirlingS1[n, k]*(Sum[(j - 1)!*StirlingS2[k, j], {j, 1, k}])^2, {k, 1, n}]/(n-1)!, {n, 1, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)

Table[-(-1)^n + Sum[StirlingS1[n, k]*PolyLog[1-k, 2]^2, {k, 2, n}]/(n-1)!, {n, 1, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)

CROSSREFS

Cf. A101370, A000629.

Sequence in context: A201304 A173998 A135743 * A104032 A130406 A225236

Adjacent sequences:  A123111 A123112 A123113 * A123115 A123116 A123117

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 28 2006

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)