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A206227 Number of partitions of n^2+n into parts not greater than n. 4
1, 1, 4, 19, 108, 674, 4494, 31275, 225132, 1662894, 12541802, 96225037, 748935563, 5900502806, 46976736513, 377425326138, 3056671009814, 24930725879856, 204623068332997, 1688980598900228, 14012122025369431, 116784468316023069, 977437078888272796, 8212186058546599006 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..382 (first 150 terms from Alois P. Heinz)

FORMULA

a(n) = [x^(n^2+n)] Product_{k=1..n} 1/(1 - x^k).

a(n) ~ c * d^n / n^2, where d = 9.1533701924541224619485302924013545... = A258268, c = 0.3572966225745094270279188015952797... . - Vaclav Kotesovec, Sep 07 2014

MAPLE

T:= proc(n, k) option remember;

      `if`(n=0 or k=1, 1, T(n, k-1) + `if`(k>n, 0, T(n-k, k)))

    end:

seq(T(n^2+n, n), n=0..20); # Vaclav Kotesovec, May 25 2015 after Alois P. Heinz

MATHEMATICA

Table[SeriesCoefficient[Product[1/(1-x^k), {k, 1, n}], {x, 0, n*(n+1)}], {n, 0, 20}] (* Vaclav Kotesovec, May 25 2015 *)

PROG

(PARI) {a(n)=polcoeff(prod(k=1, n, 1/(1-x^k+x*O(x^(n^2+n)))), n^2+n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A173519, A206226, A206240, A107379, A258268.

Sequence in context: A182541 A241839 A218183 * A091643 A323620 A306183

Adjacent sequences:  A206224 A206225 A206226 * A206228 A206229 A206230

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 05 2012

STATUS

approved

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Last modified May 27 20:36 EDT 2020. Contains 334667 sequences. (Running on oeis4.)