A135756 a(n) = Sum_{k=0..n} C(n,k) * 2^(k*(k-1)).

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

G. C. Greubel, Table of n, a(n) for n = 0..50

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

Adjacent sequences: A135753 A135754 A135755 * A135757 A135758 A135759

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2007

Status

approved