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A215915 E.g.f.: exp( Sum_{n>=1} A000041(n)*x^n/n ), where A000041(n) is the number of partitions of n. 6
1, 1, 3, 13, 79, 579, 5209, 53347, 628257, 8223481, 119473291, 1893056781, 32677209103, 606930554923, 12109058077809, 257638964244739, 5830359141736129, 139638723615395697, 3531794326401241747, 93977250969358226701, 2625647922067519041231, 76809884197769914248211 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note that exp( Sum_{k>=1} A183610(n,k)*x^k/k ) is an integer series for row n>=1; the partition numbers, which forms row 0 of table A183610, is the exception.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..432

FORMULA

a(n) = (n-1)!*sum(p(i+1)*a(n-i-1)/(n-i-1)!,i,0,n-1), a(0)=1, where p(i) is the number of partitions of n. - Vladimir Kruchinin, Feb 27 2015

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 79*x^4/4! + 579*x^5/5! + 5209*x^6/6! +  ...

such that log(A(x)) = x + 2*x^2/2 + 3*x^3/3 + 5*x^4/4 + 7*x^5/5 + 11*x^6/6 + 15*x^7/7 + 22*x^8/8 + ... + A000041(n)*x^n/n + ...

MATHEMATICA

nmax = 20; CoefficientList[Series[E^Sum[PartitionsP[k]*x^k/k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)

PROG

(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n+1, numbpart(m)*x^m/m+x*O(x^n))), n)}

for(n=0, 31, print1(a(n), ", "))

(Maxima)

a(n):=if n=0 then 1 else (n-1)!*sum(num_partitions(i+1)*a(n-i-1)/(n-i-1)!, i, 0, n-1); /* Vladimir Kruchinin, Feb 27 2015 */

CROSSREFS

Cf. A183610, A000041, A058892, A293731, A293839.

Sequence in context: A141762 A062872 A288954 * A159312 A213527 A261601

Adjacent sequences:  A215912 A215913 A215914 * A215916 A215917 A215918

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 26 2012

STATUS

approved

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Last modified July 7 14:14 EDT 2020. Contains 335495 sequences. (Running on oeis4.)