A048514 a(n) = T(0,n)+T(1,n-1)+...+T(n,0), array T given by A048505.

1, 3, 13, 54, 190, 587, 1659, 4412, 11244, 27785, 67089, 159106, 371930, 859159, 1964855, 4454968, 10025240, 22411221, 49804909, 110097630, 242217766, 530575683, 1157623603, 2516577524, 5452589700, 11777599457

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-42,96, -129,102,-44,8).

Programs

Mathematica

LinearRecurrence[{10,-42,96,-129,102,-44,8},{1,3,13,54,190,587,1659},30] (* Harvey P. Dale, Aug 01 2022 *)

PARI

T(k, n) = (n^2 + (4*k+1)*n + (2*k)^2) * 2^(n-2) - k^2 + 1
a(n) = sum(k=0, n, T(k,n-k)) \\ Colin Barker, Feb 25 2015

Formula

G.f.: (8*x^5-37*x^4+46*x^3-25*x^2+7*x-1) / ((x-1)^4*(2*x-1)^3). - Colin Barker, Feb 25 2015

Extensions

Typo in a(25) fixed by Colin Barker, Feb 25 2015