A240434 Binomial transform of the sum of the first n even squares (A002492).

0, 4, 28, 128, 480, 1600, 4928, 14336, 39936, 107520, 281600, 720896, 1810432, 4472832, 10895360, 26214400, 62390272, 147062784, 343670784, 796917760, 1835008000, 4198498304, 9550430208, 21609054208, 48653926400, 109051904000, 243403849728, 541165879296

Offset

0,2

Comments

The inverse binomial transform of a(n) is A002492(n) = 2n(n+1)(2n+1)/3.

Links

Table of n, a(n) for n=0..27.

Formula

Conjecture: a(n) = (2^(n-1)*n*(5+6*n+n^2))/3. G.f.: -4*x*(x-1) / (2*x-1)^4. - Colin Barker, Apr 06 2014

a(n) = (-1)^n * Sum_{k=0..floor(n/2)} binomial(n-k, k) * (-4)^(n-k) * (n-k). - Joseph M. Shunia, Jul 20 2022

Mathematica

Table[Sum[2 Binomial[n, k] k (k + 1) (2 k + 1)/3, {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A002492.

Sequence in context: A231581 A223115 A296381 * A270275 A296638 A270721

Adjacent sequences: A240431 A240432 A240433 * A240435 A240436 A240437

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 04 2014

Status

approved