A336010 a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-5,k) * a(k) * a(n-k-5).

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 66, 148, 374, 1052, 3156, 9724, 31096, 104124, 366696, 1355624, 5220120, 20763160, 84944720, 357759200, 1557192440, 7029575320, 32929457880, 159764303320, 800509163360, 4132518624560, 21953331512080, 119966645509440

Offset

0,7

Comments

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

Links

Table of n, a(n) for n=0..32.

Formula

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.

Mathematica

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}]
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]!

Crossrefs

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

Sequence in context: A370340 A308032 A100138 * A180208 A100139 A274860

Adjacent sequences: A336007 A336008 A336009 * A336011 A336012 A336013

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2020

Status

approved