A393536 G.f. A(x) satisfies: A(x) = 1 + x * A(2*x/(1 - 2*x)^2) / (1 - 2*x).

1, 1, 4, 32, 472, 12272, 562304, 46177664, 6960985728, 1973396337920, 1073942111214592, 1139234954223038464, 2380123287434280220672, 9857337060965758382256128, 81241345954032205383763492864, 1335431499390414491203019844255744, 43836743072987217081264113915533230080

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{k=0..n-1} binomial(n+k-1,n-k-1) * a(k).

Mathematica

nmax = 16; A[_] = 0; Do[A[x_] = 1 + x A[2 x/(1 - 2 x)^2]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = 2^(n - 1) Sum[Binomial[n + k - 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

Crossrefs

Cf. A000110, A125273, A165193, A390837, A392468, A392532, A392538, A393535.

Sequence in context: A192500 A192486 A037964 * A089285 A209197 A086906

Adjacent sequences: A393533 A393534 A393535 * A393537 A393539 A393540

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2026

Status

approved