A056003 a(n) = (n+1)*binomial(n+8, 8).

1, 18, 135, 660, 2475, 7722, 21021, 51480, 115830, 243100, 481338, 906984, 1637610, 2848860, 4796550, 7845024, 12503007, 19468350, 29683225, 44401500, 65270205, 94427190, 134617275, 189329400, 262957500, 360988056, 490217508, 659002960, 877549860, 1158240600

Offset: 0

Author

Barry E. Williams, Jun 12 2000

Keywords

• nonn
• easy

Comments

Original name: A second-order recursive sequence.

References

• Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Partial sums of A056117.

Cf. A093644 ((9, 1) Pascal, column m=9).

Cf. A000142, A007318, A052206, A245334, A254142 (partial sums).

Programs

Haskell

a056003 n = (n + 1) * a007318' (n + 8) 8
-- Reinhard Zumkeller, Aug 31 2014

Maple

a:=n->(sum((numbcomp(n,9)), j=9..n)):seq(a(n), n=9..35); # Zerinvary Lajos, Aug 26 2008

Mathematica

a[n_] := (n+1)*Binomial[n+8, 8]; Array[a, 50, 0] (* Amiram Eldar, Jan 15 2023 *)

PARI

a(n) = (n+1)*binomial(n+8, 8) \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (1+8*x)/(1-x)^10.

a(n) = A245334(n+8,8)/A000142(8). - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=0} 1/a(n) = 4*Pi^2/3 - 266681/22050.

Sum_{n>=0} (-1)^n/a(n) = 2*Pi^2/3 - 38656*log(2)/105 + 611409/2450. (End)