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A172434 G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = [ Sum_{n>=0} x^n/n!^4 ]^3. 3
1, 3, 51, 1785, 67635, 2973753, 146591529, 7735733883, 430208938035, 24954576411225, 1496639801457801, 92241539987122683, 5816057121183700521, 373854785336483200155, 24431647104881328618315, 1619654401178752389082785 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..n} C(n,k)^4 * Sum_{j=0..k} C(k,j)^4 = Sum_{k=0..n} C(n,k)^4 * A005260(k).

EXAMPLE

G.f.: A(x) = 1 + 3*x + 51*x^2/2!^4 + 1785*x^3/3!^4 + 67635*x^4/4!^4 +...

A(x)^(1/3) = 1 + x + x^2/2!^4 + x^3/3!^4 + x^4/4!^4 +...

PROG

(PARI) {a(n)=if(n<0, 0, n!^4*polcoeff(sum(m=0, n, x^m/m!^4+x*O(x^n))^3, n))}

(PARI) {a(n)=sum(k=0, n, binomial(n, k)^4*sum(j=0, k, binomial(k, j)^4))}

CROSSREFS

Cf. A002893, A005260, A141057, A180350, A336270.

Sequence in context: A126685 A246693 A187666 * A210676 A105639 A003028

Adjacent sequences:  A172431 A172432 A172433 * A172435 A172436 A172437

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 20 2011

STATUS

approved

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)