login
A050404
Partial sums of A051878.
3
1, 14, 77, 280, 798, 1932, 4158, 8184, 15015, 26026, 43043, 68432, 105196, 157080, 228684, 325584, 454461, 623238, 841225, 1119272, 1469930, 1907620, 2448810, 3112200, 3918915, 4892706, 6060159, 7450912
OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
FORMULA
a(n) = binomial(n+5, 5)*(4*n+3)/3.
G.f.: (1+7*x)/(1-x)^7.
E.g.f.: (360 +4680*x +9000*x^2 +5400*x^3 +1275*x^4 +123*x^5 +4*x^6 )*exp(x)/360. - G. C. Greubel, Aug 30 2019
MAPLE
seq((4*n+3)*binomial(n+5, 5)/3, n=0..40); # G. C. Greubel, Aug 30 2019
MATHEMATICA
Table[(4*n+3)*Binomial[n+5, 5]/3, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011, modified by G. C. Greubel, Aug 30 2019 *)
PROG
(PARI) vector(40, n, (4*n-1)*binomial(n+4, 5)/3) \\ G. C. Greubel, Aug 30 2019
(Magma) [(4*n+3)*Binomial(n+5, 5)/3: n in [0..40]]; // G. C. Greubel, Aug 30 2019
(Sage) [(4*n+3)*binomial(n+5, 5)/3 for n in (0..30)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..40], n-> (4*n+3)*Binomial(n+5, 5)/3); # G. C. Greubel, Aug 30 2019
CROSSREFS
Cf. A051878.
Cf. A093565 ((8, 1) Pascal, column m=6).
Sequence in context: A022706 A269495 A085462 * A335757 A044201 A044582
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 21 1999
EXTENSIONS
Corrected by T. D. Noe, Nov 09 2006
STATUS
approved