A319835 O.g.f. A(x) satisfies: [x^n] 1/(1-x)^(n^3) / exp( n*A(x) ) = 0 for n >= 1.

1, 11, 615, 93042, 26367840, 11896260357, 7790323334052, 6971417293247088, 8168310247001057784, 12135241152923019699370, 22293293737202063158881716, 49628657379474422562364524042, 131669704562621977069760097583577, 410540174242581740798413641858906388

Offset

1,2

Comments

It is remarkable that this sequence should consist entirely of integers.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Example

G.f.: A(x) = x + 11*x^2 + 615*x^3 + 93042*x^4 + 26367840*x^5 + 11896260357*x^6 + 7790323334052*x^7 + 6971417293247088*x^8 + ...
The table of coefficients of x^k/k! in 1/(1-x)^(n^3)/exp(n*A(x)) begins
n=1: [1, 0, -21, -3688, -2231679, -3163366296, -8564468186765, ...];
n=2: [1, 6, 0, -7796, -4645296, -6462213792, -17357826387392, ...];
n=3: [1, 24, 537, 0, -7554843, -10352322288, -27117968407587, ...];
n=4: [1, 60, 3576, 197048, 0, -15133017984, -39314407194560, ...];
n=5: [1, 120, 14415, 1715200, 188756385, 0, -54226299944825, ...];
n=6: [1, 210, 44184, 9292212, 1935426096, 373568674464, 0, ...]; ...
in which the coefficient of x^n in the n-th row forms a diagonal of zeros.
RELATED SERIES.
exp(A(x)) = 1 + x + 23*x^2/2! + 3757*x^3/3! + 2249353*x^4/4! + 3176162021*x^5/5! + 8585203977031*x^6/6! + 39325009824213793*x^7/7! + ...

Prog

(PARI) {a(n) = my(A=[1], m); for(i=1, n+1, A=concat(A, 0); m=#A; A[m] = Vec( 1/(1-x +x^2*O(x^m))^(m^3) * exp(-m*x*Ser(A)) )[m+1]/m ); polcoeff( x*Ser(A), n)}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A317342, A319836, A319831.

Sequence in context: A262015 A275572 A115737 * A288549 A237187 A201175

Adjacent sequences: A319832 A319833 A319834 * A319836 A319837 A319838

Keyword

nonn

Author

Paul D. Hanna, Sep 30 2018

Status

approved