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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
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. A093564 ((7, 1) Pascal, column m=5).
Sequence in context: A212682 A212134 A071270 * A212065 A121693 A190297
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Dec 14 1999
STATUS
approved

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