A348662 a(n) = Sum_{m=0..n} (-1)^m * ( Sum_{k=0..m} binomial(n,k) )^2.

1, -3, 8, -30, 128, -518, 2048, -8172, 32768, -131142, 524288, -2096900, 8388608, -33555356, 134217728, -536867480, 2147483648, -8589947462, 34359738368, -137438904852, 549755813888, -2199023440308, 8796093022208, -35184371383400, 140737488355328

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = -(4/(n-1)) * ( 2 * (n-2) * a(n-1) + (5 * n - 14) *a(n-2) + 8 * (n-3) * a(n-3) + 16 * (n-4) * a(n-4) ) for n > 3.

a(n) ~ (-1)^n * 2^(2*n-1). - Vaclav Kotesovec, Nov 01 2021

Mathematica

a[n_] := Sum[(-1)^m * Sum[Binomial[n, k], {k, 0, m}]^2, {m, 0, n}]; Array[a, 25, 0] (* Amiram Eldar, Oct 28 2021 *)

Prog

(PARI) a(n) = sum(m=0, n, (-1)^m*sum(k=0, m, binomial(n, k))^2);

Crossrefs

Sum_{m=0..n} ( Sum_{k=0..m} (-1)^m * binomial(n,k) )^E: (-1)^n * A011782(n) (E=1), this sequence (E=2), A348457 (E=3).

Cf. A003583.

Sequence in context: A213860 A360991 A361135 * A162560 A293250 A096161

Adjacent sequences: A348659 A348660 A348661 * A348663 A348664 A348665

Keyword

sign

Author

Seiichi Manyama, Oct 28 2021

Status

approved