A183236 Sums of multinomial coefficients to the 4th power.

1, 1, 17, 1378, 354065, 221300626, 286871431922, 688780254549829, 2821284379712638737, 18510450092641988146882, 185104666826030540618018642, 2710117456989714966261367339909, 56196998736058707145628074314226034

Offset

0,3

Comments

Equals sums of the 4th power of terms in rows of the triangle of multinomial coefficients (A036038).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..140

Formula

G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = Product_{n>=1} 1/(1 - x^n/n!^4).

a(n) ~ c * (n!)^4, where c = Product_{k>=2} 1/(1-1/(k!)^4) = 1.067493570155257423039762074691753715853526744464586468822554194836450214299287... . - Vaclav Kotesovec, Feb 19 2015

Example

G.f.: A(x) = 1 + x + 17*x^2/2!^4 + 1378*x^3/3!^4 + 354065*x^4/4!^4 +...
A(x) = 1/((1-x)*(1-x^2/2!^4)*(1-x^3/3!^4)*(1-x^4/4!^4)*...).

Prog

(PARI) {a(n)=n!^4*polcoeff(1/prod(k=1, n, 1-x^k/k!^4 +x*O(x^n)), n)}

Crossrefs

Cf. A036038, A005651, A183240, A183235, A183237, A183238.

Sequence in context: A316746 A067409 A219562 * A007410 A203229 A269791

Adjacent sequences: A183233 A183234 A183235 * A183237 A183238 A183239

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2011

Status

approved