OFFSET
0,2
COMMENTS
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Murray R.Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = binomial(n+3, 3)*(7*n+4)/4.
a(n) = (7*n+4)*binomial(n+3, 3)/4.
G.f.: (1+6*x)/(1-x)^5.
a(n) = A080852(7,n). - R. J. Mathar, Jul 28 2016
E.g.f.: (4! + 240*x + 288*x^2 + 88*x^3 + 7*x^4)*exp(x)/4!. - G. C. Greubel, Aug 29 2019
MAPLE
seq((7*n+4)*binomial(n+3, 3)/4, n=0..40); # G. C. Greubel, Aug 29 2019
MATHEMATICA
Table[(7*n+4)*Binomial[n+3, 3]/4, {n, 0, 40)] (* G. C. Greubel, Aug 29 2019 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 11, 45, 125, 280}, 40] (* Harvey P. Dale, May 18 2023 *)
PROG
(Magma) /* A000027 convolved with A001106 (excluding 0): */ A001106:=func<n | n*(7*n-5)/2>; [&+[(n-i+1)*A001106(i): i in [1..n]]: n in [1..36]]; // Bruno Berselli, Dec 07 2012
(PARI) vector(40, n, (7*n-3)*binomial(n+2, 3)/4) \\ G. C. Greubel, Aug 29 2019
(Sage) [(7*n+4)*binomial(n+3, 3)/4 for n in (0..40)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..40], n-> (7*n+4)*Binomial(n+3, 3)/4); # G. C. Greubel, Aug 29 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Dec 07 1999
STATUS
approved