OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..57
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n, k)*2^(k^2) where Stirling1 numbers are described by A008275.
EXAMPLE
E.g.f.: A(x) = 1 + 2*x + 14*x^2/2! + 468*x^3/3! + 62628*x^4/4! +...
A(x) = 1 + 2*log(1+x) + 2^4*log(1+x)^2/2! + 2^9*log(1+x)^3/3! +...
MATHEMATICA
Table[Sum[StirlingS1[n, k]*2^(k^2), {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, May 02 2018 *)
PROG
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, 2^(k^2)*log(1+x+x*O(x^n))^k/k!), n)}
(PARI) {a(n)=sum(k=0, n, 2^(k^2)*n!*polcoeff(binomial(x, n), k))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 25 2009
STATUS
approved