A344556 a(n) = [x^n] 2 / (1 - (2*n - 1)*x + sqrt(1 - 2*x - 3*x^2)).

1, 1, 5, 34, 315, 3741, 54531, 944035, 18934763, 431773963, 11030464423, 312023972228, 9680623848325, 326823162461823, 11926991260987869, 467837288974848642, 19628089812933434547, 877052336082168698715, 41581946832665768549007, 2084818230218269733957646

Offset

0,3

Comments

Main diagonal of A344567.

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{j=0..n} (n - 1)^j*binomial(n, j)*hypergeom([(j - n)/2, (j - n + 1)/2], [j + 2], 4).

a(n) ~ n^n * (1 + 1/n + 1/(2*n^2) - 4/(3*n^3) - 119/(24*n^4) - 1249/(120*n^5) - ...). - Vaclav Kotesovec, May 24 2021

Maple

aList := proc(len) 2 / (1 - (2*n - 1)*x + sqrt(1 - 2*x - 3*x^2));
seq(coeff(series(%, x, len+2), x, n), n = 0..len) end: aList(19);

Mathematica

Unprotect[Power]; 0^0 := 1;
a[n_] := Sum[(n-1)^j Binomial[n, j] Hypergeometric2F1[(j - n)/2, (j - n + 1)/2, j + 2, 4], {j, 0, n}]; Table[a[n], {n, 0, 19}]

Crossrefs

Cf. A344567.

Sequence in context: A258179 A068475 A097817 * A303175 A357422 A197714

Adjacent sequences: A344553 A344554 A344555 * A344557 A344558 A344559

Keyword

nonn

Author

Peter Luschny, May 24 2021

Status

approved