A381278 -id:A381278 - cp's OEIS frontend

A381286 Expansion of e.g.f. 1/(1 - sin(3*x) / 3).

1, 1, 2, -3, -48, -339, -1008, 10737, 237312, 2362041, 5432832, -318158523, -7615254528, -87216236379, 173049219072, 33959321252217, 851545449234432, 9561733579228401, -129701862228492288, -9445723672920941043, -239815723596207095808, -2109465061216228379619

Offset: 0

Seiichi Manyama, Feb 18 2025

sign

Cf. A000111, A381285.

Cf. A136630, A352638, A381278.

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, k!*(3*I)^(n-k)*a136630(n, k));

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * binomial(n,2*k+1) * a(n-2*k-1).

a(n) = Sum_{k=0..n} k! * (3*i)^(n-k) * A136630(n,k), where i is the imaginary unit.

A381343 Expansion of e.g.f. exp( sin(sqrt(2)*x) / sqrt(2) ).

Original entry on oeis.org

1, 1, 1, -1, -7, -15, 25, 287, 721, -2847, -30255, -61697, 682761, 5861713, 3105193, -258188513, -1681060063, 4623681473, 135471132705, 564325398271, -6357495670375, -89817656595791, -84337394884167, 7820620314702879, 67277670159083761, -322108989883888479

Offset: 0

Seiichi Manyama, Feb 20 2025

sign

Cf. A002017, A009210, A009229, A351891, A351892, A381277, A381278, A381280, A381344.

Cf. A136630.

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (-2)^((n-k)/2)*a136630(n, k));

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * binomial(n-1,2*k) * a(n-2*k-1).

a(n) = Sum_{k=0..n} (-2)^((n-k)/2) * A136630(n,k).

cp's OEIS Frontend

A381286 Expansion of e.g.f. 1/(1 - sin(3*x) / 3).

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