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A135756
a(n) = Sum_{k=0..n} C(n,k) * 2^(k*(k-1)).
4
1, 2, 7, 80, 4381, 1069742, 1080096067, 4405584869660, 72092808533798521, 4723015159635987920282, 1237987266193328694390243007, 1298087832233881093828346620725800
OFFSET
0,2
COMMENTS
The square root of the g.f. of this sequence is an integer series (cf. A261594).
LINKS
Ville Salo, Decidability and Universality of Quasiminimal Subshifts, arXiv:1411.6644 [math.DS], 2014-2015.
FORMULA
a(n) ~ 2^(n*(n-1)). - Vaclav Kotesovec, Nov 27 2017
EXAMPLE
G.f.: A(x) = 1 + 2*x + 7*x^2 + 80*x^3 + 4381*x^4 + 1069742*x^5 +...
MATHEMATICA
Table[Sum[Binomial[n, k]*2^(2*Binomial[k, 2]), {k, 0, n}], {n, 0, 25}] (* G. C. Greubel, Nov 07 2016 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*2^(k*(k-1)))}
CROSSREFS
Cf. A261594; variants: A006896, A135755.
Sequence in context: A326262 A071409 A232041 * A263368 A208806 A319144
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 27 2007
STATUS
approved