A292782 a(n) = E(2n,n)/2, where E(n,x) is the Euler polynomial.

0, 1, 63, 6306, 990550, 227890755, 72524317341, 30560156566660, 16483798503292716, 11080974333713379525, 9085235508141504416155, 8924963654575108415598246, 10349560274697013067017980738, 13989200573862071630368836403591, 21802322447828101388917112243376825

Offset: 1

Author

Vladimir Shevelev, Sep 23 2017

Keywords

• nonn

Comments

Conjecture. For n >= 2, a(n) is divisible by n(n-1)/2, moreover, for odd n, a(n) is divisible by n^2(n-1)/2.

References

• M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.

Crossrefs

Cf. A291897, A291982.

Programs

Mathematica

Table[EulerE[2 n, n]/2, {n, 15}] (* Michael De Vlieger, Sep 23 2017 *)

Formula

a(n) = (-1)^n*(1^(2*n) - 2^(2*n) + ... +(-1)^n*(n-1)^(2*n)).

a(n) ~ c * n^(2*n), where c = A349003/2 = 1/(1 + exp(2)) = 0.1192029220221175559402708586976... - Vaclav Kotesovec, Nov 05 2021

Extensions

More terms from Peter J. C. Moses, Sep 23 2017