A270918 Largest coefficient of (1+x+...+x^n)^(2*n).

1, 2, 19, 580, 38165, 4395456, 786588243, 202384723528, 70886845397481, 32458256583753952, 18832730699014127291, 13507852690353224821652, 11738630472138500287398379, 12155701820213424461220851360, 14790850878997102285050287114419

Offset: 0

Author

Vaclav Kotesovec, Mar 26 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..210

Crossrefs

Cf. A077047.

Cf. A002426, A005190, A005191, A018901, A025012, A025013, A025014, A025015.

Programs

Mathematica

Table[Max[CoefficientList[Expand[Sum[x^k, {k, 0, n}]^(2n)], x]], {n, 0, 20}]

PARI

a(n) = vecmax(Vec((sum(k=0,n,x^k))^(2*n))); \\ Michel Marcus, Apr 01 2016

Formula

a(n) ~ exp(2) * sqrt(3/Pi) * n^(2*n - 3/2).

Extensions

Typo in formula corrected by Vaclav Kotesovec, Dec 10 2021