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A136649 Binomial transform of A014070: a(n) = Sum_{k=0..n} C(n,k)*C(2^k,k). 1
1, 3, 11, 81, 2089, 211107, 76211147, 95054910473, 410422012327681, 6211807332775516467, 334327967114349983723899, 64835852334793138873642165105, 45812640033676518721399820389451657 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: A(x) = (1/(1-x))*Sum_{n>=0} [log(1 + (2^n-1)*x) - log(1-x)]^n / n!.
From Vaclav Kotesovec, Jul 02 2016: (Start)
a(n) ~ binomial(2^n,n).
a(n) ~ 2^(n^2) / n!.
a(n) ~ 2^(n^2 - 1/2) * exp(n) / (sqrt(Pi) * n^(n+1/2)). (End)
MATHEMATICA
Table[Sum[Binomial[n, k]*Binomial[2^k, k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*binomial(2^k, k))}
(PARI) /* Using the g.f.: */ {a(n)=local(X=x+x*O(x^n)); polcoeff(sum(k=0, n, (log(1+(2^k-1)*X)-log(1-X))^k/k!)/(1-X), n)}
CROSSREFS
Cf. A014070 (C(2^n, n)), A134173.
Partial sums of A180687.
Sequence in context: A232468 A099341 A129114 * A342058 A062580 A335968
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Charles R Greathouse IV, Oct 28 2009
STATUS
approved

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Last modified December 7 05:10 EST 2023. Contains 367629 sequences. (Running on oeis4.)