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 A318115 Number of compositions of n into exactly n nonnegative parts <= seven. 2
 1, 1, 3, 10, 35, 126, 462, 1716, 6427, 24229, 91828, 349570, 1335698, 5119856, 19678452, 75814560, 292695291, 1132074847, 4385740683, 17015510820, 66102536360, 257103599280, 1001078753370, 3901733646660, 15220908863866, 59427261280126, 232201593611796 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1669 FORMULA a(n) = [x^n] ((x^8-1)/(x-1))^n. a(n) <= A088218(n) with equality only for n < 8. a(n) = Sum_{k=0..floor(n/8)} (-1)^k * binomial(n,k) * binomial(2*n-8*k-1,n-8*k). - Ilya Gutkovskiy, Nov 03 2021 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 7)))) end: a:= n-> b(n\$2): seq(a(n), n=0..30); CROSSREFS Column k=7 of A305161. Cf. A088218. Sequence in context: A122068 A099908 A363781 * A318116 A167403 A318117 Adjacent sequences: A318112 A318113 A318114 * A318116 A318117 A318118 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 17 2018 STATUS approved

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Last modified October 4 19:37 EDT 2023. Contains 365888 sequences. (Running on oeis4.)