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A166993 G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/(2*n) ), where A005260(n) = Sum_{k=0..n} C(n,k)^4. 5
1, 1, 5, 32, 266, 2499, 25765, 283084, 3264502, 39077898, 481942608, 6089941550, 78523226064, 1029859481949, 13704960309415, 184688556173542, 2516342539576510, 34617557176739174, 480336524752492608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

Self-convolution yields A166992.

a(n) ~ c * 16^n / n^(5/2), where c = 0.14011467789446087641913961305130549385534145578464604013551918158... - Vaclav Kotesovec, Nov 27 2017

EXAMPLE

G.f.: A(x) = 1 + x + 5*x^2 + 32*x^3 + 266*x^4 + 2499*x^5 + 25765*x^6 +...

log(A(x)) = x + 9*x^2/2 + 82*x^3/3 + 905*x^4/4 + 10626*x^5/5 + 131922*x^6/6 + 1697508*x^7/7 +...+ A005260(n)/2*x^n/n +...

MATHEMATICA

a[n_] := Sum[(Binomial[n, k])^4, {k, 0, n}]; f[x_] := Sum[a[n]*x^n/(2*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)/2*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A005260, A166991, A166992.

Sequence in context: A198598 A215916 A068102 * A328055 A265130 A305407

Adjacent sequences:  A166990 A166991 A166992 * A166994 A166995 A166996

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 17 2009

STATUS

approved

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Last modified September 18 03:36 EDT 2021. Contains 347504 sequences. (Running on oeis4.)