A194722 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting ten doublets into the initially empty word.

0, 1, 92378, 19319845, 560198962, 6507351113, 44731364266, 218878998733, 844131474530, 2730108129937, 7711583225338, 19564269083381, 45486599105938, 98378219490265, 200201768681162, 386776488742813, 714420272913346, 1268930908616993, 2177477525153050

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: x * (1 +92368*x +18396110*x^2 +371157402*x^3 +1763669368*x^4 +2567824154*x^5 +1206169122*x^6 +163325950*x^7 +4293143*x^8 +4862*x^9) / (x-1)^10.

a(0) = 0, a(n) = 1 +(18 +(152 +(798 +(2907 +(7752 +(15504 +(23256 +(25194 +16796*(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) * (n-1)) * (n-1) for n>0.

Example

a(1) = 1: a^20 (with 1-ary alphabet {a}).

Maple

a:= n-> `if`(n=0, 0, (x-> 1+(18+(152+(798+(2907+(7752+(15504+(23256+
                     (25194+16796*x)*x)*x)*x)*x)*x)*x)*x)*x)(n-1)):
seq(a(n), n=0..30);

Crossrefs

Row n=10 of A183134.

Sequence in context: A116122 A116134 A318631 * A140932 A208623 A294857

Adjacent sequences: A194719 A194720 A194721 * A194723 A194724 A194725

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2011

Status

approved