A049144 - OEIS

%I #10 Jan 02 2021 11:26:00

%S 1,1,2,4,10,24,64,167,460,1256,3532,9910,28280,80756,232984,673371,

%T 1958982,5710900,16722156,49061276,144387320,425674212,1257774336,

%U 3721938064,11032243612,32740524236,97287632048,289369653892

%N Revert transform of (1 + x - 2x^2 + x^3)/(1 + 2x).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F Recurrence: 31*(n-2)*(n-1)*n*(472*n^3 - 4608*n^2 + 14891*n - 15930)*a(n) = 4*(n-2)*(n-1)*(12272*n^4 - 138216*n^3 + 563902*n^2 - 975864*n + 591975)*a(n-1) + 72*(n-2)*(1416*n^5 - 19488*n^4 + 106149*n^3 - 285989*n^2 + 380822*n - 200250)*a(n-2) - 8*(35872*n^6 - 619248*n^5 + 4419892*n^4 - 16684488*n^3 + 35101288*n^2 - 38981571*n + 17829450)*a(n-3) - 48*(n-4)*(3*n - 13)*(3*n - 11)*(472*n^3 - 3192*n^2 + 7091*n - 5175)*a(n-4). - _Vaclav Kotesovec_, Jan 02 2021

%t Rest[CoefficientList[InverseSeries[Series[x*(1 + x - 2x^2 + x^3)/(1 + 2x), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)

%K nonn

%O 1,3

%A _Olivier Gérard_