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A055740 Sum of fourth powers of coefficients in full expansion of (z1+z2+...+zn)^n. 2
1, 1, 18, 1785, 591460, 495872505, 882463317636, 2956241639184631, 17088644286346128840, 159584255348964655673745, 2286523844910576580400966980, 48220116744252542032928364578451, 1446485887751234540636003724054342864, 59981372975740557234356339667492583487125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

FORMULA

a(n) is coefficient of x^n in expansion of n!^4*(1+x/1!^4+x^2/2!^4+x^3/3!^4+...+x^n/n!^4)^n.

a(n) ~ c * d^n * (n!)^4 / sqrt(n), where d = 1.511958716403..., c = 0.6632048858... . - Vaclav Kotesovec, Aug 20 2014

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(b(n-j, i-1)*binomial(n, j)^3/j!, j=0..n)))

    end:

a:= n-> n!*b(n$2):

seq(a(n), n=0..20);  # Alois P. Heinz, Jul 21 2014

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[b[n-j, i-1]*Binomial[n, j]^3 /j!, {j, 0, n}]]]; a[n_] := n!*b[n, n]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 24 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A033935.

Column k=4 of A245397.

Sequence in context: A064347 A253121 A067303 * A072477 A249332 A019522

Adjacent sequences:  A055737 A055738 A055739 * A055741 A055742 A055743

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 09 2000

EXTENSIONS

a(0)=1 inserted by Alois P. Heinz, Jul 21 2014

STATUS

approved

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Last modified September 24 22:31 EDT 2017. Contains 292441 sequences.