cp's OEIS Frontend

A237653 O.g.f.: Sum_{n>=0} x^n*Product_{k=1..n} (k + x).

%I A237653 #7 Oct 28 2014 15:49:56
%S A237653 1,1,3,9,36,176,1030,7039,55098,486346,4780445,51787405,613045468,
%T A237653 7873065045,109021348618,1619197654575,25675094145535,432908683794379,
%U A237653 7733991639921585,145933532935469016,2900112108790279902,60543749629794205640,1324677739541613767983,30312375400027348522996
%N A237653 O.g.f.: Sum_{n>=0} x^n*Product_{k=1..n} (k + x).
%C A237653 Equals antidiagonal sums of the triangle of unsigned Stirling numbers of the first kind (A008275).
%H A237653 Vaclav Kotesovec, <a href="/A237653/b237653.txt">Table of n, a(n) for n = 0..400</a>
%e A237653 G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 36*x^4 + 176*x^5 + 1030*x^6 + 7039*x^7 +...
%e A237653 where
%e A237653 A(x) = 1 + x*(1+x) + x^2*(1+x)*(2+x) + x^3*(1+x)*(2+x)*(3+x) + x^4*(1+x)*(2+x)*(3+x)*(4+x) +...
%o A237653 (PARI) {a(n)=polcoeff(sum(k=0, n, x^k*prod(j=1, k, j+x +x*O(x^n))), n)}
%o A237653 for(n=0,30,print1(a(n),", "))
%Y A237653 Cf. A124380, A008275, A130534.
%K A237653 nonn
%O A237653 0,3
%A A237653 _Paul D. Hanna_, May 11 2014