A381409 -id:A381409 - cp's OEIS frontend

A381410 E.g.f. A(x) satisfies A(x) = exp( 2 * x * cos(x * A(x)) ).

1, 2, 4, 2, -128, -2118, -23456, -125046, 2962432, 134260082, 3203705344, 43519495186, -465102608384, -58643045328086, -2434321489723392, -60275924271785062, -100012292095737856, 89170947715367242466, 5992924139510968483840, 233532153884059053483042

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Seiichi Manyama, Feb 23 2025

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As stated in the comment of A185951, A185951(n,0) = 0^n.

Cf. A185951, A381409.

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*I^(n-k)*a185951(n, k));

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381409.

a(n) = 2 * Sum_{k=0..n} (2*n-2*k+2)^(k-1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.

cp's OEIS Frontend

A381410 E.g.f. A(x) satisfies A(x) = exp( 2 * x * cos(x * A(x)) ).

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