A254142 a(n) = (9*n+10)*binomial(n+9,9)/10.

1, 19, 154, 814, 3289, 11011, 32032, 83512, 199342, 442442, 923780, 1830764, 3468374, 6317234, 11113784, 18958808, 31461815, 50930165, 80613390, 125014890, 190285095, 284712285, 419329560, 608658960, 871616460, 1232604516, 1722822024, 2381824984

Offset: 0

Author

Bruno Berselli, Jan 26 2015

Keywords

• nonn
• easy

Comments

Partial sums of A056003.

If n is of the form 8*k+2*(-1)^k-1 or 8*k+2*(-1)^k-2 then a(n) is odd.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A000581, A001287, A056003.

Cf. sequences of the type (k*n+k+1)*binomial(n+k,k)/(k+1): A000217 (k=1), A000330 (k=2), A001296 (k=3), A034263 (k=4), A051946 (k=5), A034265 (k=6), A034266 (k=7), A056122 (k=8), this sequence (k=9).

Programs

GAP

List([0..30], n-> (9*n+10)*Binomial(n+9,9)/10); # G. C. Greubel, Aug 28 2019

Magma

[(9*n+10)*Binomial(n+9,9)/10: n in [0..30]];

Maple

seq((9*n+10)*binomial(n+9,9)/10, n=0..30); # G. C. Greubel, Aug 28 2019

Mathematica

Table[(9n+10)Binomial[n+9, 9]/10, {n, 0, 30}]

PARI

vector(30, n, n--; (9*n+10)*binomial(n+9, 9)/10)

Sage

[(9*n+10)*binomial(n+9,9)/10 for n in (0..30)]

Formula

G.f.: (1 + 8*x)/(1-x)^11.

a(n) = Sum_{i=0..n} (i+1)*A000581(i+8).

a(n+1) = 8*A001287(n+10) + A001287(n+11).