A160710 - OEIS

%I #5 May 03 2018 07:04:15

%S 1,2,14,468,62628,32916240,68221619760,561512669071200,

%T 18431003537355665760,2417187863502316739842560,

%U 1267541812947815891035704645120,2658386273978048637324643356687805440

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

%H G. C. Greubel, <a href="/A160710/b160710.txt">Table of n, a(n) for n = 0..57</a>

%F a(n) = Sum_{k=0..n} Stirling1(n, k)*2^(k^2) where Stirling1 numbers are described by A008275.

%e E.g.f.: A(x) = 1 + 2*x + 14*x^2/2! + 468*x^3/3! + 62628*x^4/4! +...

%e A(x) = 1 + 2*log(1+x) + 2^4*log(1+x)^2/2! + 2^9*log(1+x)^3/3! +...

%t Table[Sum[StirlingS1[n, k]*2^(k^2), {k, 0, n}], {n, 0, 30}] (* _G. C. Greubel_, May 02 2018 *)

%o (PARI) {a(n)=n!*polcoeff(sum(k=0,n,2^(k^2)*log(1+x+x*O(x^n))^k/k!),n)}

%o (PARI) {a(n)=sum(k=0,n,2^(k^2)*n!*polcoeff(binomial(x, n), k))}

%Y Cf. A006025, A006024.

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 25 2009