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A304394 O.g.f. A(x) satisfies: [x^n] exp( n^4 * x ) * (1 - x*A(x)) = 0 for n>0. 5
1, 112, 76221, 152978176, 673315202500, 5508710472669120, 75300988091046198131, 1595530380622638283804672, 49561200934127182294698009969, 2161539625780059763174286300310000, 127884966535158110582342524738392563401, 9979510403062963314615799917574094659938048, 1003426348756281631241586585232930123009989117616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

INVERT transform of A304324.

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) = (n+1)^(4*n+4)/(n+1)! - Sum_{k=1..n} (n+1)^(4*k)/k! * a(n-k) for n>0 with a(0)=1.

EXAMPLE

O.g.f.: A(x) = 1 + 112*x + 76221*x^2 + 152978176*x^3 + 673315202500*x^4 + 5508710472669120*x^5 + 75300988091046198131*x^6 + ...

such that the coefficient of x^n in exp(n^4*x) * (1 - x*A(x)) = 0 for n>0.

PROG

(PARI) /* From formula: [x^n] exp( n^4*x ) * (1 - x*A(x)) = 0 */

{a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); m=#A; A[m] = Vec( exp(x*m^4 +x^2*O(x^m)) * (1 - x*Ser(A)) )[m+1] ); A[n+1]}

for(n=0, 25, print1( a(n), ", "))

CROSSREFS

Cf. A304324, A304396, A107668, A107675, A304395.

Sequence in context: A063409 A051366 A051363 * A210292 A270146 A184898

Adjacent sequences:  A304391 A304392 A304393 * A304395 A304396 A304397

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 12 2018

STATUS

approved

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Last modified June 6 17:33 EDT 2020. Contains 334831 sequences. (Running on oeis4.)