The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051877 Partial sums of A051740. 5
 1, 12, 57, 182, 462, 1008, 1974, 3564, 6039, 9724, 15015, 22386, 32396, 45696, 63036, 85272, 113373, 148428, 191653, 244398, 308154, 384560, 475410, 582660, 708435, 855036, 1024947, 1220842, 1445592, 1702272, 1994168, 2324784, 2697849, 3117324, 3587409 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of triangular numbers (A000217) and enneagonal numbers (A001106). - Bruno Berselli, Jul 21 2015 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index to sequences related to pyramidal numbers Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = C(n+4, 4)*(7*n+5)/5. G.f.: (1+6*x)/(1-x)^6. From Wesley Ivan Hurt, May 02 2015: (Start) a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6). a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120. (End) E.g.f.: (5! +1320*x +2040*x^2 +920*x^3 +145*x^4 +7*x^5)*exp(x)/5! MAPLE A051877:=n->binomial(n+4, 4)*(7*n+5)/5: seq(A051877(n), n=0..40); # Wesley Ivan Hurt, May 02 2015 MATHEMATICA Table[(n+1)(n+2)(n+3)(n+4)(7n+5)/120, {n, 0, 40}] (* Vincenzo Librandi, May 03 2015 *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 12, 57, 182, 462, 1008}, 40] (* Harvey P. Dale, May 05 2022 *) PROG (Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120 : n in [0..40]]; // Wesley Ivan Hurt, May 02 2015 (PARI) vector(40, n, (7*n-2)*binomial(n+3, 4)/5) \\ G. C. Greubel, Aug 29 2019 (Sage) [(7*n+5)*binomial(n+4, 4)/5 for n in (0..40)] # G. C. Greubel, Aug 29 2019 (GAP) List([0..40], n-> (7*n+5)*Binomial(n+4, 4)/5); # G. C. Greubel, Aug 29 2019 CROSSREFS Cf. A051740; A000217, A001106. Cf. A093564 ((7, 1) Pascal, column m=5). Sequence in context: A212682 A212134 A071270 * A212065 A121693 A190297 Adjacent sequences: A051874 A051875 A051876 * A051878 A051879 A051880 KEYWORD nonn,easy AUTHOR Barry E. Williams, Dec 14 1999 STATUS approved

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

Last modified March 1 08:00 EST 2024. Contains 370430 sequences. (Running on oeis4.)