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 A261739 Number of partitions of n where each part i is marked with a word of length i over a quinary alphabet whose letters appear in alphabetical order. 2
 1, 5, 40, 235, 1470, 8001, 45865, 241870, 1307055, 6783210, 35510502, 181665635, 934801705, 4741017595, 24118500815, 121693135003, 614889556920, 3091596201560, 15557885702390, 78054925105630, 391798489621630, 1963104427709830, 9838685572501515 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) ~ c * 5^n, where c = Product_{k>=2} 1/(1 - (k+1)*(k+2)*(k+3)*(k+4)/(24*5^k)) = 4.1548340497015786311470026968208254860294132084317763408428889184148319... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021 G.f.: Product_{k>=1} 1 / (1 - binomial(k+4,4)*x^k). - Ilya Gutkovskiy, May 09 2021 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+4, 4)))) end: a:= n-> b(n\$2): seq(a(n), n=0..30); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, b[n - i, i]*Binomial[i + 4, 4]]]]; a[n_] := b[n, n]; a /@ Range[0, 30] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *) CROSSREFS Column k=5 of A261718. Sequence in context: A271092 A273653 A081364 * A230744 A269822 A043019 Adjacent sequences: A261736 A261737 A261738 * A261740 A261741 A261742 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 30 2015 STATUS approved

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Last modified June 18 21:09 EDT 2024. Contains 373487 sequences. (Running on oeis4.)