A009767 Expansion of e.g.f. tan(x^2)/2 in odd powers of x^2.

1, 120, 241920, 2352430080, 70008319180800, 4981141593037209600, 724337282211580477440000, 193082117289145211195228160000, 87097726450270042926290105794560000, 62534967622066352401869341275560345600000, 68083350599600621793249530921443071413452800000

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Formula

a(n) = A000182(n+1)*(4*n+2)!/(2*(2*n+1)!). - Andrew Howroyd, Jan 12 2025

Example

x^2/2! + 120*x^6/6! + 241920*x^10/10! + 2352430080*x^14/14! ...

Mathematica

Tan[ x^2 ]/2 (* [ x^(4n+2) ] *)

Prog

(PARI) seq(n)={my(A=O(x^(4*n+3))); Vec(substpol(serlaplace( tan(x^2 + A)/2 )/x^2, x^4, x))} \\ Andrew Howroyd, Jan 12 2025

Crossrefs

Cf. A000182, A024348.

Sequence in context: A172805 A008701 A158043 * A181750 A003789 A325024

Adjacent sequences: A009764 A009765 A009766 * A009768 A009769 A009770

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested 03/97.

a(9) onwards from Andrew Howroyd, Jan 12 2025

Status

approved