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!)
 A053581 First differences of the Poly-Bernoulli numbers B_n^(k) with k=-2 (A027649). 5
 1, 3, 10, 32, 100, 308, 940, 2852, 8620, 25988, 78220, 235172, 706540, 2121668, 6369100, 19115492, 57362860, 172121348, 516429580, 1549419812, 4648521580, 13946089028, 41839315660, 125520044132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the second differences of A001047. Equals sum of "terms added" to current row of the triangle version of A038573 to get the next row. a(3) = 32 sum of (3, 7, 7, 15) = terms appended to row 2 of the triangle in A038573. - Gary W. Adamson, Jun 04 2009 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-6). FORMULA a(n) = 5*a(n-1) - 6*a(n-2) + C(2,2-n), n>1, with a(0)=1, a(1)=3, where C(2, 2-n)=1 for n=2 and =0 for n>2. From Paul Barry, Jun 26 2003: (Start) Binomial transform of A000975(n+1). G.f.: (1-x)^2/((1-2*x)*(1-3*x)). a(n) = 4*3^n/3 + 0^n/6 - 2^n/2. (End) a(n) = Sum_{k=0..n+1} binomial(n+1, k) * Sum_{j=0..floor(k/2)} A001045(k-2*j). - Paul Barry, Apr 17 2005 E.g.f.: (1 - 3*exp(2*x) + 8*exp(3*x))/6. - G. C. Greubel, May 16 2019 MATHEMATICA CoefficientList[Series[(1-x)^2/((1-2x)(1-3x)), {x, 0, 30}], x]  (* Harvey P. Dale, Apr 22 2011 *) PROG (MAGMA) [4*3^n/3+0^n/6-2^n/2: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011 (PARI) vector(30, n, n--; 4*3^(n-1) +(0^n -3*2^n)/6) \\ G. C. Greubel, May 16 2019 (Sage) [4*3^(n-1) +(0^n -3*2^n)/6 for n in (0..30)] # G. C. Greubel, May 16 2019 (GAP) List([0..30], n-> 4*3^(n-1) +(0^n -3*2^n)/6) # G. C. Greubel, May 16 2019 CROSSREFS Cf. A001047, A027649. Cf. A001045. Cf. A038573. - Gary W. Adamson, Jun 04 2009 Sequence in context: A104270 A038731 A244762 * A247595 A092822 A017935 Adjacent sequences:  A053578 A053579 A053580 * A053582 A053583 A053584 KEYWORD easy,nonn AUTHOR Barry E. Williams, Jan 18 2000 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 June 21 02:05 EDT 2021. Contains 345342 sequences. (Running on oeis4.)