cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A160710 E.g.f.: Sum_{n>=0} 2^(n^2)*log(1+x)^n/n!.

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%I A160710 #5 May 03 2018 07:04:15
%S A160710 1,2,14,468,62628,32916240,68221619760,561512669071200,
%T A160710 18431003537355665760,2417187863502316739842560,
%U A160710 1267541812947815891035704645120,2658386273978048637324643356687805440
%N A160710 E.g.f.: Sum_{n>=0} 2^(n^2)*log(1+x)^n/n!.
%H A160710 G. C. Greubel, <a href="/A160710/b160710.txt">Table of n, a(n) for n = 0..57</a>
%F A160710 a(n) = Sum_{k=0..n} Stirling1(n, k)*2^(k^2) where Stirling1 numbers are described by A008275.
%e A160710 E.g.f.: A(x) = 1 + 2*x + 14*x^2/2! + 468*x^3/3! + 62628*x^4/4! +...
%e A160710 A(x) = 1 + 2*log(1+x) + 2^4*log(1+x)^2/2! + 2^9*log(1+x)^3/3! +...
%t A160710 Table[Sum[StirlingS1[n, k]*2^(k^2), {k, 0, n}], {n, 0, 30}] (* _G. C. Greubel_, May 02 2018 *)
%o A160710 (PARI) {a(n)=n!*polcoeff(sum(k=0,n,2^(k^2)*log(1+x+x*O(x^n))^k/k!),n)}
%o A160710 (PARI) {a(n)=sum(k=0,n,2^(k^2)*n!*polcoeff(binomial(x, n), k))}
%Y A160710 Cf. A006025, A006024.
%K A160710 nonn
%O A160710 0,2
%A A160710 _Paul D. Hanna_, May 25 2009