A204473 Number of 9-element subsets that can be chosen from {1,2,...,18*n+9} having element sum 81*n+45.

1, 94257, 9853759, 182262067, 1537408202, 8262875230, 33131331832, 108130342498, 302954110225, 754561227653, 1711557426281, 3597716377411, 7099506906934, 13283048544410, 23746473266386, 40814224081470, 67780377968751, 109208632376183, 171297152624647

Offset

0,2

Comments

a(n) is the number of partitions of 81*n+45 into 9 distinct parts <= 18*n+9.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: -(910*x^30 +1040804*x^29 +38021156*x^28 +382272336*x^27 +1924406509*x^26 +6310497232*x^25 +15598550757*x^24 +31691324994*x^23 +55644068089*x^22 +87101380417*x^21 +124235349095*x^20 +163834246902*x^19 +201423850605*x^18 +231972434360*x^17 +250948109605*x^16 +255267409282*x^15 +244185313288*x^14 +219577712922*x^13 +185287461384*x^12 +146192435862*x^11 +107203950569*x^10 +72278724244*x^9 +44015118309*x^8 +23603015876*x^7 +10732396387*x^6 +3881615945*x^5 +1000947039*x^4 +152795052*x^3 +9570989*x^2 +94254*x+1) / ((x^4+x^3+x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+1)*(x^2+1)^2*(x+1)^4*(x-1)^9).

Example

a(0) = 1 because there is 1 9-element subset that can be chosen from {1,2,...,9} having element sum 45: {1,2,3,4,5,6,7,8,9}.

Maple

a:= n-> (Matrix(31, (i, j)-> `if`(i=j-1, 1, `if`(i=31, [1, -3, 1, 5, -6, 1, 5, -8, 2, 9, -11, 0, 11, -11, 1, 11, -11, -1, 11, -11, 0, 11, -9, -2, 8, -5, -1, 6, -5, -1, 3][j], 0)))^n.
<<1, 94257, 9853759, 182262067, 1537408202, 8262875230, 33131331832, 108130342498, 302954110225, 754561227653, 1711557426281, 3597716377411, 7099506906934, 13283048544410, 23746473266386, 40814224081470, 67780377968751,
109208632376183, 171297152624647, 262317027786495, 393133642429336, 577820819931050, 834378155041412, 1185562499279422, 1659845127394359, 2292506656080729, 3126882354024441, 4215771021760211, 5623021191591966, 7425308933006994, 9714122125363850>>)[1, 1]: seq(a(n), n=0..50);

Crossrefs

Bisection of column k=9 of A204459.

Sequence in context: A209514 A029754 A258892 * A031675 A254977 A238143

Adjacent sequences: A204470 A204471 A204472 * A204474 A204475 A204476

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 16 2012

Status

approved