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A337553
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (4*k-3) * a(n-k).
2
1, 1, 7, 45, 439, 5157, 73455, 1217101, 23066311, 491680437, 11645898655, 303422639517, 8624098330359, 265546702327813, 8805478883825359, 312844282877905389, 11855836533424581415, 477380986427269453653, 20352680600044759742463, 915923521948522369041469
OFFSET
0,3
FORMULA
E.g.f.: 1 / (exp(x) * (3 - 4*x) - 2).
a(n) ~ n! * c * 2^(2*n+1) / ((1-c) * (3 - 4*c)^(n+1)), where c = -LambertW(-exp(-3/4)/2). - Vaclav Kotesovec, Aug 31 2020
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (4 k - 3) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(Exp[x] (3 - 4 x) - 2), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (3 - 4*x) - 2)))} \\ Andrew Howroyd, Aug 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 31 2020
STATUS
approved