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

1, 42, 345, 1597, 5436, 15217, 37148, 81901, 166819, 318857, 578413, 1004224, 1679522, 2719666, 4281488, 6574614, 9875045, 14541308, 21033513, 29935679, 41981720, 58085511, 79375484, 107234235, 143343655, 189736131, 248852397, 323606650, 417459582, 534500016

Offset: 1

Author

Alois P. Heinz, Aug 18 2012

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• W. C. Yang, Derivatives are essentially integer partitions, Discrete Mathematics, 222(1-3), July 2000, 235-245.

Crossrefs

Row n=10 of A022818.

Programs

Maple

a:= n-> n*(n+1)*(136656+(-412380+(209204+(203887+(40826+(3148+(98+n)*
        n)*n)*n)*n)*n)*n)/362880:
seq(a(n), n=1..40);

Mathematica

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 *)

Formula

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.

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.