A135748 -id:A135748 - cp's OEIS frontend

A173403 Inverse binomial transform of A002416.

1, 1, 13, 469, 63577, 33231721, 68519123173, 562469619451069, 18442242396353040817, 2417685638793025070212561, 1267626422541873052658376446653, 2658442047546208031914776455678477989, 22300713297142388711251601783864453690641417

Offset: 0

Brian Drake, Feb 17 2010

nonn

a(n) is the number of n X n matrices of 0's and 1's with the property that there is no index k such that both the k-th column and the k-th row consist of all zeros.

a(n) is the number of binary relations on n labeled vertices with no vertex of indegree and outdegree = 0. - Geoffrey Critzer, Oct 02 2012

E. A. Bender and S. G. Williamson, Foundations of Combinatorics with Applications, Dover, 2005, exercise 4.1.6.

Brian Drake, Table of n, a(n) for n = 0..50

Cf. A002416, A135748, A287065, A048291.

N:=8: seq( sum(binomial(n,i)*2^((n-i)^2)*(-1)^(i), i=0..n), n=0..N);

Table[Sum[(-1)^k Binomial[n,k] 2^(n-k)^2,{k,0,n}],{n,0,20}]  (* Geoffrey Critzer, Oct 02 2012 *)

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

a(n) ~ 2^(n^2). - Vaclav Kotesovec, Oct 30 2017

A006898 a(n) = Sum_{k=0..n} C(n,k)2^(k(k+1)/2).

Original entry on oeis.org

1, 3, 13, 95, 1337, 38619, 2310533, 283841911, 70927591153, 35812691480115, 36383765777442685, 74185239630793429775, 303119284294591169426729, 2479814853198140771706795531, 40599509058360322571947638063605

Offset: 0

Colin Mallows

nonn

First differences of A006896.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Cf. A006896, A006897, A135748.

Table[Sum[Binomial[n,k]2^((k(k+1))/2),{k,0,n}],{n,0,20}] (* Harvey P. Dale, Apr 01 2023 *)

a(n)=sum(k=0,n,binomial(n,k)*2^(k*(k+1)/2)) \\ Paul D. Hanna, Apr 10 2009

a(n) ~ 2^(n*(n+1)/2). - Vaclav Kotesovec, Nov 27 2017

Formula and more terms from Vladeta Jovovic, Sep 20 2003

Edited by N. J. A. Sloane, Apr 12 2009 at the suggestion of Vladeta Jovovic

cp's OEIS Frontend

A173403 Inverse binomial transform of A002416.

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A006898 a(n) = Sum_{k=0..n} C(n,k)2^(k(k+1)/2).

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cp's OEIS Frontend

A173403 Inverse binomial transform of A002416.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A006898 a(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2).

Views

Author

Keywords

Comments

References

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A006898 a(n) = Sum_{k=0..n} C(n,k)2^(k(k+1)/2).