cp's OEIS Frontend

A215628 Number of terms in 10th derivative of a function composed with itself n times.

%I A215628 #13 Jan 27 2017 19:12:29
%S A215628 1,42,345,1597,5436,15217,37148,81901,166819,318857,578413,1004224,
%T A215628 1679522,2719666,4281488,6574614,9875045,14541308,21033513,29935679,
%U A215628 41981720,58085511,79375484,107234235,143343655,189736131,248852397,323606650,417459582,534500016
%N A215628 Number of terms in 10th derivative of a function composed with itself n times.
%H A215628 Alois P. Heinz, <a href="/A215628/b215628.txt">Table of n, a(n) for n = 1..1000</a>
%H A215628 W. C. Yang, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00412-4">Derivatives are essentially integer partitions</a>, Discrete Mathematics, 222(1-3), July 2000, 235-245.
%F A215628 G.f.: -(4*x^7-34*x^6+110*x^5-161*x^4+83*x^3+30*x^2-32*x-1)*x/(x-1)^10.
%F A215628 a(n) = n*(n+1)*(n^7 +98*n^6 +3148*n^5 +40826*n^4 +203887*n^3 +209204*n^2 -412380*n +136656) / 362880.
%p A215628 a:= n-> n*(n+1)*(136656+(-412380+(209204+(203887+(40826+(3148+(98+n)*
%p A215628         n)*n)*n)*n)*n)*n)/362880:
%p A215628 seq(a(n), n=1..40);
%t A215628 CoefficientList[Series[-(4*x^7 - 34*x^6 + 110*x^5 - 161*x^4 + 83*x^3 + 30*x^2 - 32*x - 1)/(x - 1)^10, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jan 27 2017 *)
%Y A215628 Row n=10 of A022818.
%K A215628 nonn,easy
%O A215628 1,2
%A A215628 _Alois P. Heinz_, Aug 18 2012