A385309
Expansion of e.g.f. 1/(1 - 3 * x * cosh(x))^(1/3).
Original entry on oeis.org
1, 1, 4, 31, 328, 4485, 75520, 1509347, 34916224, 917703145, 27011107840, 880133628231, 31451749424128, 1223047891889837, 51414400611438592, 2323391075748100555, 112315439676217262080, 5783449255108473820497, 316034972288791445241856, 18265740423344520141491951
Offset: 0
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a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k)*a185951(n, k));
A352647
Expansion of e.g.f. 1/(1 - 3 * x * cos(x)).
Original entry on oeis.org
1, 3, 18, 153, 1728, 24315, 410400, 8079729, 181786752, 4601232243, 129402385920, 4003157532297, 135098815002624, 4939266681129963, 194472450526169088, 8203835046344538465, 369151362125290045440, 17649035213360472293091, 893431062200523039178752
Offset: 0
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With[{m = 18}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*x*Cos[x]), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*cos(x))))
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a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));
A352648
Expansion of e.g.f. 1/(1 - 2 * x * cosh(x)).
Original entry on oeis.org
1, 2, 8, 54, 480, 5290, 70080, 1083614, 19145728, 380552274, 8404669440, 204182993542, 5411361939456, 155365918497530, 4803852288901120, 159142710151610670, 5623576097060290560, 211138456468635968674, 8393550198348236193792, 352212802264773650385110
Offset: 0
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With[{m = 19}, Range[0, m]! * CoefficientList[Series[1/(1 - 2*x*Cosh[x]), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x*cosh(x))))
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a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));
Showing 1-3 of 3 results.