The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A181084 Expansion of g.f.: exp( Sum_{n>=1} [Sum_{k=0..n} binomial(n,k)^(n+k+1) * x^k] * x^n/n ). 3
 1, 1, 2, 10, 92, 1367, 87090, 20385333, 6633475836, 4096297538926, 14834973644512627, 119919823546238898903, 1273371038284317852447990, 41086272137585936052959008420, 6982122140549374036504235218052104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjecture: this sequence consists entirely of integers. LINKS G. C. Greubel, Table of n, a(n) for n = 0..70 EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 92*x^4 + 1367*x^5 + 87090*x^6 + ... The logarithm of g.f. A(x) begins: log(A(x)) = x + 3*x^2/2 + 25*x^3/3 + 327*x^4/4 + 6336*x^5/5 + 513657*x^6/6 + ... + A181085(n)*x^n/n + ... and equals the series: log(A(x)) = (1 + x)*x + (1 + 2^4*x + x^2)*x^2/2 + (1 + 3^5*x + 3^6*x^2 + x^3)*x^3/3 + (1 + 4^6*x + 6^7*x^2 + 4^8*x^3 + x^4)*x^4/4 + (1 + 5^7*x + 10^8*x^2 + 10^9*x^3 + 5^10*x^4 + x^5)*x^5/5 + (1 + 6^8*x + 15^9*x^2 + 20^10*x^3 + 15^11*x^4 + 6^12*x^5 + x^6)*x^6/6 + ... MATHEMATICA With[{m=20}, CoefficientList[Series[Exp[Sum[Sum[Binomial[n, k]^(n+k+1)*x^(n+k)/n, {k, 0, n}], {n, m+1}]], {x, 0, m}], x]] (* G. C. Greubel, Apr 05 2021 *) PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^(m+k+1)*x^k)*x^m/m) + x*O(x^n)), n)} (Magma) m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( Exp( (&+[ (&+[ Binomial(n, k)^(n+k+1)*x^(n+k)/n : k in [0..n]]): n in [1..m+1]]) ) )); // G. C. Greubel, Apr 05 2021 (Sage) m=20; def A181084_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( exp( sum( sum( binomial(n, k)^(n+k+1)*x^(n+k)/n for k in (0..n) ) for n in (1..m+1)) ) ).list() A181084_list(m) # G. C. Greubel, Apr 05 2021 CROSSREFS Cf. A181085 (log), variants: A181080, A181082. Sequence in context: A289020 A195415 A336271 * A063385 A293709 A063393 Adjacent sequences: A181081 A181082 A181083 * A181085 A181086 A181087 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 28 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 01:02 EDT 2024. Contains 373402 sequences. (Running on oeis4.)