A363385 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^2 / k ).

1, 1, 0, 1, 2, 2, 4, 11, 14, 29, 66, 115, 222, 493, 944, 1884, 4020, 8175, 16618, 35198, 73220, 151844, 321036, 676778, 1421828, 3016813, 6407344, 13589888, 28962702, 61853827, 132073646, 282752030, 606492428, 1301587833, 2797816706, 6023460551, 12978238202, 27995493484

Offset

1,5

Links

Table of n, a(n) for n=1..38.

Mathematica

nmax = 38; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[A[x^k]^2/k, {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = a[2] = 1; g[n_] := g[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[d g[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 38}]

Prog

(PARI) seq(n)=my(p=x+x^2+O(x^3)); for(n=1, n\2, my(m=serprec(p, x)-1); p = x + x^2*exp(sum(k=1, m\2, subst(p + O(x^(m\k+1)), x, x^k)^2/k))); Vec(p + O(x*x^n)) \\ Andrew Howroyd, May 30 2023

Crossrefs

Cf. A005750, A007562, A363386.

Sequence in context: A220800 A220786 A280673 * A280531 A072074 A052338

Adjacent sequences: A363382 A363383 A363384 * A363386 A363387 A363388

Keyword

nonn

Author

Ilya Gutkovskiy, May 30 2023

Status

approved