A278934 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*binomial(2*k,k)^2.

1, 3, 29, 303, 3501, 42663, 538769, 6977547, 92078989, 1232902023, 16700233689, 228356672547, 3147087003201, 43659275921667, 609117615688149, 8539863624592023, 120242239301247309, 1699411957967345127, 24098616839012623769, 342754384909199620803

Offset: 0

Author

Seiichi Manyama, Dec 02 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..853

Crossrefs

Cf. A248586.

Cf. Sum_{k = 0..n} (-1)^(n-k)*binomial(n, k)*binomial(2*k, k)^m: A002426 (m=1), this sequence (m=2), A276537 (m=3).

Programs

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[n,k]*Binomial[2*k,k]^2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 02 2016 *)
Table[(-1)^n*HypergeometricPFQ[{1/2, 1/2, -n}, {1, 1}, 16], {n, 0, 20}] (* Vaclav Kotesovec, Dec 02 2016 *)

Formula

Recurrence: n^2*a(n) = (13*n^2 - 13*n + 3)*a(n-1) + 29*(n-1)^2*a(n-2) + 15*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Dec 02 2016

a(n) ~ 15^(n+1) / (16*Pi*n). - Vaclav Kotesovec, Dec 02 2016