A258465 Number of partitions of n into parts of exactly 10 sorts which are introduced in ascending order.

1, 56, 1762, 41143, 795657, 13499449, 208050040, 2979881876, 40300054520, 520576172762, 6478447651345, 78185947269684, 919805200917658, 10591351937396242, 119764715367192468, 1333512940732309728, 14652754322423701707, 159182411488944508232

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