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A294119
Expansion of e.g.f.: exp(2*((1+x)^2 - 1)).
3
1, 4, 20, 112, 688, 4544, 31936, 236800, 1841408, 14943232, 126063616, 1101983744, 9954734080, 92714156032, 888502796288, 8746003922944, 88294183469056, 912920984944640, 9655688415674368, 104353064578711552, 1151244577906098176, 12953223477921316864
OFFSET
0,2
LINKS
FORMULA
E.g.f.: exp(2*((1+x)^2 - 1)).
a(n) ~ 2^(n - 1/2) * n^(n/2) * exp(-1 + 2*sqrt(n) - n/2). - Vaclav Kotesovec, Oct 23 2017
a(n) = 4*a(n-1)+4*(n-1)*a(n-2). - Robert Israel, Jun 16 2020
MAPLE
f:= rectoproc({a(n)=4*a(n-1)+4*(n-1)*a(n-2), a(0)=1, a(1)=4}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Jun 16 2020
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(2*((1+x)^2 - 1)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2017 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(2*((1+x)^2-1))))
CROSSREFS
Column k=2 of A294118.
Sequence in context: A212326 A192624 A209200 * A245375 A362223 A108447
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 23 2017
STATUS
approved