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 A258465 Number of partitions of n into parts of exactly 10 sorts which are introduced in ascending order. 3
 1, 56, 1762, 41143, 795657, 13499449, 208050040, 2979881876, 40300054520, 520576172762, 6478447651345, 78185947269684, 919805200917658, 10591351937396242, 119764715367192468, 1333512940732309728, 14652754322423701707, 159182411488944508232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 10,2 COMMENTS In general, column k>1 of A256130 is asymptotic to c*k^n, where c = 1/(k!*Product_{n>=1} (1-1/k^n)) = 1/(k!*QPochhammer[1/k, 1/k]). - Vaclav Kotesovec, Jun 01 2015 LINKS Alois P. Heinz, Table of n, a(n) for n = 10..1000 FORMULA a(n) ~ c * 10^n, where c = 1/(10!*Product_{n>=1} (1-1/10^n)) = 1/(10!*QPochhammer[1/10, 1/10]) = 0.0000003096292864992979803727261336621564... . - Vaclav Kotesovec, Jun 01 2015 MAPLE b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))) end: T:= (n, k)-> add(b(n\$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k): a:= n-> T(n, 10): seq(a(n), n=10..30); MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k b[n - i, i, k]]]]; T[n_, k_] := Sum[b[n, n, k - i] (-1)^i/(i! (k - i)!), {i, 0, k}]; Table[T[n, 10], {n, 10, 30}] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *) CROSSREFS Column k=10 of A256130. Cf. A320552. Sequence in context: A017719 A234761 A290607 * A050989 A333067 A140406 Adjacent sequences: A258462 A258463 A258464 * A258466 A258467 A258468 KEYWORD nonn AUTHOR Alois P. Heinz, May 30 2015 STATUS approved

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Last modified August 11 11:53 EDT 2024. Contains 375069 sequences. (Running on oeis4.)