A258462 Number of partitions of n into parts of exactly 7 sorts which are introduced in ascending order.

1, 29, 492, 6401, 70880, 704676, 6490951, 56524414, 471750267, 3810085912, 29989229859, 231255237311, 1754111872429, 13128442913712, 97189645384884, 713050007285941, 5192646586465458, 37581376345088462, 270593146237918806, 1939929376872664097

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

a(n) ~ c * 7^n, where c = 1/(7!*Product_{n>=1} (1-1/7^n)) = 1/(7!*QPochhammer[1/7, 1/7]) = 0.0002371101666331046535758625585353... . - 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, 7):
seq(a(n), n=7..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, 7], {n, 7, 30}] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Column k=7 of A256130.

Cf. A320549.

Sequence in context: A182014 A261540 A173986 * A320550 A211833 A022753

Adjacent sequences: A258459 A258460 A258461 * A258463 A258464 A258465

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved