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A304395 O.g.f. A(x) satisfies: [x^n] exp( n^5 * x ) * (1 - x*A(x)) = 0 for n>0. 5
1, 480, 2245320, 43083161600, 2331513459843750, 287128730182879382976, 69929145078323834449039740, 30496052356323314014140611297280, 22113924320024426907851753695581691875, 25177421842925471123473548283955430812500000, 42994775028354266041451477298870703788676694998956, 106089234738948935762581435147478647028049918327743508480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

INVERT transform of A304325.

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) = (n+1)^(5*n+5)/(n+1)! - Sum_{k=1..n} (n+1)^(5*k)/k! * a(n-k) for n>0 with a(0)=1.

EXAMPLE

O.g.f.: A(x) = 1 + 480*x + 2245320*x^2 + 43083161600*x^3 + 2331513459843750*x^4 + 287128730182879382976*x^5 + 69929145078323834449039740*x^6 + ...

such that the coefficient of x^n in exp(n^5*x) * (1 - x*A(x)) = 0 for n>0.

PROG

(PARI) /* From formula: [x^n] exp( n^5*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^5 +x^2*O(x^m)) * (1 - x*Ser(A)) )[m+1] ); A[n+1]}

for(n=0, 20, print1( a(n), ", "))

CROSSREFS

Cf. A304325, A304397, A107668, A107675, A304394.

Sequence in context: A289638 A289744 A287933 * A269759 A317174 A020286

Adjacent sequences:  A304392 A304393 A304394 * A304396 A304397 A304398

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 12 2018

STATUS

approved

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Last modified May 26 02:43 EDT 2020. Contains 334613 sequences. (Running on oeis4.)