The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A196795 a(n) = Sum_{k=0..n} binomial(n,k)*3^k*(k+1)^(n-k). 1
 1, 4, 22, 145, 1096, 9259, 85924, 865183, 9364864, 108173827, 1325589676, 17149360111, 233271228880, 3324545097475, 49493784653644, 767665750130839, 12376226335249024, 206967901014192643, 3583561993192959436, 64136093489935863583, 1184711492540805987856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA O.g.f.: Sum_{n>=0} 3^n*x^n/(1 - (n+1)*x)^(n+1). E.g.f.: exp(x + 3*x*exp(x)). MATHEMATICA Table[Sum[Binomial[n, k]3^k (k+1)^(n-k), {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Nov 12 2012 *) PROG (PARI) {a(n)=sum(k=0, n, binomial(n, k)*3^k*(k+1)^(n-k))} (PARI) {a(n)=polcoeff(sum(m=0, n, 3^m*x^m/(1-(m+1)*x+x*O(x^n))^(m+1)), n)} (PARI) {a(n)=n!*polcoeff(exp(x+3*x*exp(x+x*O(x^n))), n)} CROSSREFS Cf. A080108, A196794. Sequence in context: A081002 A222012 A057834 * A278396 A121394 A005039 Adjacent sequences:  A196792 A196793 A196794 * A196796 A196797 A196798 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 06 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)