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A006129 a(0),a(1),a(2),... satisfy Sum a(k) binomial(n,k) (k=0..n) = 2^binomial(n,2), for n=0,1,...
(Formerly M3678)
14
1, 0, 1, 4, 41, 768, 27449, 1887284, 252522481, 66376424160, 34509011894545, 35645504882731588, 73356937912127722841, 301275024444053951967648, 2471655539737552842139838345, 40527712706903544101000417059892, 1328579255614092968399503598175745633 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also labeled graphs on n unisolated nodes (inverse binomial transform of A006125).

REFERENCES

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..50

N. J. A. Sloane, Transforms

FORMULA

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

E.g.f.: A(x)/exp(x) where A(x) = Sum_{n>=0} 2^C(n,2) x^n/n!. - Geoffrey Critzer, Oct 21 2011

EXAMPLE

2^binomial(n,2) = 1 + binomial(n,2) + 4*binomial(n,3) + 41*binomial(n,4) + 768*binomial(n,5)+...

MAPLE

a:= proc(n) option remember; `if`(n=0, 1,

      2^binomial(n, 2) - add(a(k)*binomial(n, k), k=0..n-1))

    end:

seq (a(n), n=0..20);  # Alois P. Heinz, Oct 26 2012

MATHEMATICA

a=Sum[2^Binomial[n, 2] x^n/n!, {n, 0, 20}]; Range[0, 20]!CoefficientList[Series[ a/Exp[x], {x, 0, 20}], x]

CROSSREFS

Sequence in context: A230251 A001908 A192547 * A244437 A193363 A244751

Adjacent sequences:  A006126 A006127 A006128 * A006130 A006131 A006132

KEYWORD

nonn,nice,easy

AUTHOR

Colin Mallows

EXTENSIONS

More terms and additional comments from Vladeta Jovovic, Apr 09 2000

STATUS

approved

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Last modified December 21 11:25 EST 2014. Contains 252310 sequences.