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A135753 E.g.f.: A(x) = Sum_{n>=0} exp((3^n-1)/2*x)*x^n/n!. 5
1, 1, 3, 16, 153, 2536, 72513, 3571156, 303033153, 44411895376, 11247688063233, 4933176144494236, 3746180187749948193, 4933259445571307491096, 11257237602638666745470913, 44566655569041016108120599556 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k)*[(3^k-1)/2]^(n-k).
a(n) ~ c * 3^(n^2/4)*2^((n+1)/2)/sqrt(Pi*n), where c = Sum_{k = -infinity..infinity} 2^k*3^(-k^2) = 1.8862156350800186... if n is even and c = Sum_{k = -infinity..infinity} 2^(k+1/2)*3^(-(k+1/2)^2) = 1.8865940733664341... if n is odd. - Vaclav Kotesovec, Jun 25 2013
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*((3^k-1)/2)^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jun 25 2013 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(n, k)*((3^k-1)/2)^(n-k))
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp((3^k-1)/2*x)*x^k/k!), n)
CROSSREFS
Cf. variants: A001831, A135754.
Sequence in context: A086371 A229954 A228513 * A191959 A349591 A091146
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 27 2007
STATUS
approved

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Last modified July 14 12:35 EDT 2024. Contains 374318 sequences. (Running on oeis4.)