A132608 Self-convolution square-root of A062817 (offset 2); thus g.f. A(x) satisfies: A(x)^2 = Sum_{n>=2} A062817(n)*x^n, where A062817(n) = Sum_{k=0..n} (n-k)^k*k^(n-k).

1, 2, 9, 58, 469, 4530, 50491, 634790, 8861043, 135750454, 2262315973, 40726646802, 787471241647, 16275700505510, 358103286781293, 8357593147404346, 206241859929682177, 5366082228239257410

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..425

Formula

a(n) ~ exp(1) * sqrt(2*Pi/3) * n^(n + 3/2) / 2^(n+3). - Vaclav Kotesovec, Nov 22 2021

Example

A(x) = x + 2x^2 + 9x^3 + 58x^4 + 469x^5 + 4530x^6 +...+ a(n)*x^n +...
A(x)^2 = x^2 + 4x^3 + 22x^4 + 152x^5 + 1251x^6 +...+ A062817(n)*x^n +...

Mathematica

nmax = 20; CoefficientList[Series[(Sum[x^(k-2) * Sum[(k-j)^j * j^(k-j), {j, 0, k}], {k, 1, 2*nmax}])^(1/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 22 2021 *)

Prog

(PARI) {a(n)=polcoeff((sum(m=2, n+1, sum(k=0, m, (m-k)^k*k^(m-k))*x^m +x*O(x^(n+1))))^(1/2), n)}

Crossrefs

Cf. A062817, A132609.

Sequence in context: A366401 A116867 A168358 * A361598 A247329 A080834

Adjacent sequences: A132605 A132606 A132607 * A132609 A132610 A132611

Keyword

nonn

Author

Paul D. Hanna, Aug 26 2007

Status

approved