A352645 Expansion of e.g.f. exp(3 * x * cosh(x)).
1, 3, 9, 36, 189, 1068, 6669, 47568, 363897, 2976048, 26422929, 248498880, 2464625205, 25922981568, 285884886933, 3296418423552, 39795656126193, 499998631895808, 6526830528863001, 88493793850020864, 1241919513823360941, 18020032474632956928
Offset: 0
Keywords
Programs
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Mathematica
With[{m = 21}, Range[0, m]! * CoefficientList[Series[Exp[3*x*Cosh[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *) -
PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*x*cosh(x)))) -
PARI
a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
Formula
a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
a(n) = Sum_{k=0..n} 3^k * A185951(n,k). - Seiichi Manyama, Feb 18 2025