A381219 a(n) = (6^n+2^n-2*3^n)*(n-1)!/2.

1, 11, 170, 3450, 87864, 2715720, 99248400, 4200210000, 202383054720, 10949741066880, 657619863264000, 43423960900320000, 3127284944109849600, 243957907264508236800, 20493712266753293568000, 1844490309401727187200000, 177073768932670444843008000, 18061662138488384327847936000, 1950666948832313303630438400000

Offset

1,2

Comments

This is the sequence associated with the gamma-chain (see Broadhurst link).

Links

Table of n, a(n) for n=1..19.

David Broadhurst, Resurgent Integer Sequences, Rutgers Experimental Math Seminar, Feb 06 2025; Slides.

Formula

D-finite with recurrence a(n) +11*(-n+1)*a(n-1) +36*(n-1)*(n-2)*a(n-2) -36*(n-1)*(n-2)*(n-3)*a(n-3)=0. - R. J. Mathar, Feb 18 2025

Mathematica

Table[(6^n+2^n-2*3^n) (n-1)!/2, {n, 20}] (* Harvey P. Dale, Aug 13 2025 *)

Crossrefs

Cf. A379809.

Sequence in context: A233290 A167245 A331929 * A205087 A064182 A139792

Adjacent sequences: A381216 A381217 A381218 * A381220 A381221 A381222

Keyword

nonn

Author

N. J. A. Sloane, Feb 17 2024, based on an email from David Broadhurst

Status

approved