A166992 G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/n ) where A005260(n) = Sum_{k=0..n} C(n,k)^4.

1, 2, 11, 74, 621, 5850, 60212, 659712, 7583514, 90494068, 1112755389, 14022849582, 180362150901, 2360201899690, 31344689243344, 421621652965160, 5734850816825046, 78773961705345324, 1091497852618784390

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

Self-convolution of A166993.

a(n) ~ c * 16^n / n^(5/2), where c = 0.30919827904959014083681667605470681109347914449671378054261267779... - Vaclav Kotesovec, Nov 27 2017

Example

G.f.: A(x) = 1 + 2*x + 11*x^2 + 74*x^3 + 621*x^4 + 5850*x^5 + 60212*x^6 +...
log(A(x)) = 2*x + 18*x^2/2 + 164*x^3/3 + 1810*x^4/4 + 21252*x^5/5 + 263844*x^6/6 + 3395016*x^7/7 +...+ A005260(n)*x^n/n +...

Mathematica

a[n_] := Sum[(Binomial[n, k])^4, {k, 0, n}]; f[x_] := Sum[a[n]*x^n/(n), {n, 1, 75}]; CoefficientList[Series[Exp[f[x]], {x, 0, 50}], x] (* G. C. Greubel, May 30 2016 *)

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^4)*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A005260, A166990, A166993.

Sequence in context: A365153 A346424 A319743 * A058789 A212028 A324445

Adjacent sequences: A166989 A166990 A166991 * A166993 A166994 A166995

Keyword

nonn

Author

Paul D. Hanna, Nov 17 2009

Status

approved