A377521 - OEIS

%I #15 Jan 05 2025 04:22:03

%S 0,0,0,15,48,115,217,385,611,945,1366,1947,2650,3575,4663,6045,7637,

%T 9605,11836,14535,17556,21147,25125,29785,34903,40825,47282,54675,

%U 62686,71775,81571,92597,104425,117645,131768,147455,164152,182595,202161,223665,246411,271297,297550

%N Antidiagonal sums of A343053.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

%F a(n) = (2 - n)*(12*(1 + (-1)^n) - 105*n + 3*(-1)^n*n - 32*n^2 - 4*n^3)/48 for n > 1.

%F a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n > 9.

%F G.f.: x^3*(15 + 18*x - 11*x^2 - 19*x^3 + 9*x^4 + 7*x^5 - 3*x^6)/((1 - x)^5*(1 + x)^3).

%F E.g.f.: (1 - 3*x + 23*x^2/8 + x^3 + x^4/12)*cosh(x) - x*(81 - 72*x - 24*x^2 - 2*x^3)*sinh(x)/24 - 1 + 3*x.

%t LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{0,0,0,15,48,115,217,385,611,945},43]

%Y Cf. A343053.

%K nonn,easy

%O 0,4

%A _Stefano Spezia_, Jan 03 2025