A381777 Self-convolution of A001190.

0, 0, 1, 2, 3, 6, 11, 22, 44, 92, 193, 414, 896, 1966, 4347, 9700, 21787, 49262, 111976, 255824, 586996, 1352314, 3126537, 7252298, 16872307, 39360554, 92052253, 215781218, 506899243, 1193144774, 2813632668, 6646472476, 15725905877, 37264650638, 88429113569, 210123207938, 499919399933

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2545

David Serena and William J. Buchanan, Equivalence Classes Induced by Binary Tree Isomorphism -- Generating Functions, arXiv:2503.02663 [math.CO], 2025. See p. 5.

Maple

b:= proc(n) option remember; `if`(n<2, n, `if`(n::odd, 0,
      (t-> t*(1-t)/2)(b(n/2)))+add(b(i)*b(n-i), i=1..n/2))
    end:
a:= n-> add(b(j)*b(n-j), j=0..n):
seq(a(n), n=0..36);  # Alois P. Heinz, Feb 10 2026

Mathematica

terms = 40; A[_] = 0; Do[A[x_] = x + (1/2)*(A[x]^2 + A[x^2]) + O[x]^terms // Normal, terms]; CoefficientList[A[x]^2, x] (* after Jean-François Alcover, Jan 10 2018 *)

Crossrefs

Cf. A001190.

Sequence in context: A132831 A354208 A007477 * A274936 A244521 A096202

Adjacent sequences: A381774 A381775 A381776 * A381778 A381779 A381780

Keyword

nonn,easy

Author

Stefano Spezia, Mar 07 2025

Extensions

a(21) and following terms corrected by Georg Fischer, Feb 10 2026

Status

approved