A056125 a(n) = (5*n + 4)*binomial(n+7,7)/4.

1, 18, 126, 570, 1980, 5742, 14586, 33462, 70785, 140140, 262548, 469404, 806208, 1337220, 2151180, 3368244, 5148297, 7700814, 11296450, 16280550, 23088780, 32265090, 44482230, 60565050, 81516825, 108548856, 143113608, 186941656

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (1+9*x)/(1-x)^9.

a(0)=1, a(1)=18, a(2)=126, a(3)=570, a(4)=1980, a(5)=5742, a(6)=14586, a(7)=33462, a(8)=70785, a(n) = 9*a(n-1) -36*a(n-2) +84*a(n-3) -126*a(n-4) + 126*a(n-5) -84*a(n-6) +36*a(n-7) -9*a(n-8) +a(n-9). - Harvey P. Dale, Jan 18 2013

From G. C. Greubel, Jan 19 2020: (Start)

a(n) = 10*binomial(n+8,8) - 9*binomial(n+7,7).

E.g.f.: (20160 + 342720*x + 917280*x^2 + 823200*x^3 + 323400*x^4 + 62328*x^5 + 6076*x^6 + 284*x^7 + 5*x^8)*exp(x)/20160. (End)

Maple

seq( (5*n+4)*binomial(n+7, 7)/4, n=0..30); # G. C. Greubel, Jan 19 2020

Mathematica

Table[((5n+4)Binomial[n+7, 7])/4, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 18, 126, 570, 1980, 5742, 14586, 33462, 70785}, 30] (* Harvey P. Dale, Jan 18 2013 *)

Prog

(PARI) vector(31, n, (5*n-1)*binomial(n+6, 7)/4 ) \\ G. C. Greubel, Jan 19 2020
(Magma) [(5*n+4)*Binomial(n+7, 7)/4: n in [0..30]]; // G. C. Greubel, Jan 19 2020
(Sage) [(5*n+4)*binomial(n+7, 7)/4 for n in (0..30)] # G. C. Greubel, Jan 19 2020
(GAP) List([0..30], n-> (5*n+4)*Binomial(n+7, 7)/4 ); # G. C. Greubel, Jan 19 2020

Crossrefs

Cf. A052254.

Cf. A093645 ((10, 1) Pascal, column m=8).

Partial sums of A052254.

Sequence in context: A002424 A101378 A107417 * A223212 A297027 A027566

Adjacent sequences: A056122 A056123 A056124 * A056126 A056127 A056128

Keyword

easy,nonn

Author

Barry E. Williams, Jul 07 2000

Status

approved