A336010 - OEIS

%I #4 Jul 05 2020 00:01:09

%S 1,1,1,1,1,1,2,4,8,16,32,66,148,374,1052,3156,9724,31096,104124,

%T 366696,1355624,5220120,20763160,84944720,357759200,1557192440,

%U 7029575320,32929457880,159764303320,800509163360,4132518624560,21953331512080,119966645509440

%N a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-5,k) * a(k) * a(n-k-5).

%C Shifts 5 places left when e.g.f. is squared.

%F E.g.f. A(x) satisfies: A(x) = 1 + x + x^2/2 + x^3/6 + x^4/24 + Integral( Integral( Integral( Integral( Integral A(x)^2 dx) dx) dx) dx) dx.

%t a[0] = a[1] = a[2] = a[3] = a[4] = 1; a[n_] := a[n] = Sum[Binomial[n - 5, k] a[k] a[n - k - 5], {k, 0, n - 5}]; Table[a[n], {n, 0, 32}]

%t nmax = 32; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + x^3/6 + x^4/24 + Integrate[Integrate[Integrate[Integrate[Integrate[A[x]^2, x], x], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!

%Y Cf. A000142, A007558, A307972, A333497, A336009.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Jul 04 2020